3x+12×3+3x23x+12×3+3×2 Write the partial fraction decomposition of the rational expression.

# 3x+12×3+3x23x+12×3+3×2 Write the partial fraction decomposition of the rational expression.

Juliet dies by her own hand after awaking from the sleeping potion Friar Laurence gave her. When Juliet wakes up in her family mausoleum (her family, believing her dead, had placed her body there),…

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How would you solve (z-2)(z+1)=0 using the Zero Product Property?

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Write the equation in slope- intercept form for a line Slope -2/3; through (4,2)

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Pixar Studio’s Toy Story was revolutionary upon the film’s release in 1995 in terms of the studio’s use of computer generated imagery. The film was a landmark and a number of other studios and…

• MATH

x3−x+3×2+x−2×3-x+3×2+x-2 Write the partial fraction decomposition of the rational…

x3−x+3×2+x−2×3-x+3×2+x-2 Divide by applying long division method, x3−x+3×2+x−2=(x−1)+2x+1×2+x−2×3-x+3×2+x-2=(x-1)+2x+1×2+x-2 Now continue with the partial fraction of the remainder expression,…

• MATH

2×3−4×2−15x+5×2−2x−82×3-4×2-15x+5×2-2x-8 Write the partial fraction decomposition of the…

You need to decompose the fraction in simple irreducible fractions, such that: 2×3−4×2−15x+5×2−2x−8=2×3−4×2−15x+5(x−4)(x+2)2×3-4×2-15x+5×2-2x-8=2×3-4×2-15x+5(x-4)(x+2)

• MATH

x3(x+2)2(x−2)2×3(x+2)2(x-2)2 Write the partial fraction decomposition of the rational expression.

x3(x+2)2(x−2)2×3(x+2)2(x-2)2 Let x3(x+2)2(x−2)2=Ax+2+B(x+2)2+Cx−2+D(x−2)2×3(x+2)2(x-2)2=Ax+2+B(x+2)2+Cx-2+D(x-2)2 x3(x+2)2(x−2)2=A(x+2)(x−2)2+B(x−2)2+C(x−2)(x+2)2+D(x+2)2(x+2)2(x−2)2×3(x+2)2(x-2)2=A(x+2)(x-2)2+B(x-2)2+C(x-2)(x+2)2+D(x+2)2(x+2)2(x-2)2…

• MATH

x2+x+2(x2+2)2×2+x+2(x2+2)2 Write the partial fraction decomposition of the rational…

x2+x+2(x2+2)2×2+x+2(x2+2)2 Letx2+x+2(x2+2)2=Ax+Bx2+2+Cx+D(x2+2)2×2+x+2(x2+2)2=Ax+Bx2+2+Cx+D(x2+2)2 x2+x+2(x2+2)2=(Ax+B)(x2+2)+Cx+D(x2+2)2×2+x+2(x2+2)2=(Ax+B)(x2+2)+Cx+D(x2+2)2 ∴(x2+x+2)=(Ax+B)(x2+2)+Cx+D∴(x2+x+2)=(Ax+B)(x2+2)+Cx+D…

• MATH

3x+12×3+3x23x+12×3+3×2 Write the partial fraction decomposition of the rational expression.

3x+12×3+3x23x+12×3+3×2 To decompose this to partial fractions, factor the denominator. 2×3+3×2=x2(2x+3)2×3+3×2=x2(2x+3) Then, write a fraction for each factor. For the repeated factor x, form a partial…

• MATH

4×2−12x(x+1)24×2-12x(x+1)2 Write the partial fraction decomposition of the rational expression.

4×2−12x(x+1)24×2-12x(x+1)2 4×2−12x(x+1)2=A2x+Bx+1+C(x+1)24×2-12x(x+1)2=A2x+Bx+1+C(x+1)2 4×2−12x(x+1)2=A(x+1)2+B(2x)(x+1)+C(2x)2x(x+1)24×2-12x(x+1)2=A(x+1)2+B(2x)(x+1)+C(2x)2x(x+1)2 ∴(4×2−1)=A(x+1)2+B(2x)(x+1)+C(2x)∴(4×2-1)=A(x+1)2+B(2x)(x+1)+C(2x)…

• MATH

3×2−7x−2×3−x3x2-7x-2×3-x Write the partial fraction decomposition of the rational…

3×2−7x−2×3−x=3×2−7x−2x(x+1)(x−1)3×2-7x-2×3-x=3×2-7x-2x(x+1)(x-1) 3×2−7x−2×3−x=Ax+Bx+1+Cx−13×2-7x-2×3-x=Ax+Bx+1+Cx-1 Multiply through by the LDC x3−x.x3-x. 3×2−7x−2=A(x2−1)+Bx(x−1)+Cx(x+1)3×2-7x-2=A(x2-1)+Bx(x-1)+Cx(x+1)…

• MATH

5−x2x2+x−15-x2x2+x-1 Write the partial fraction decomposition of the rational expression.

5−x2x2+x−15-x2x2+x-1 =5−x2x2+2x−x−1=5-x2x2+2x-x-1 =5−x(2x(x+1)−1(x+1))=5-x(2x(x+1)-1(x+1)) =5−x(2x−1)(x+1)=5-x(2x-1)(x+1) Let 5−x2x2+x−1=A2x−1+Bx+15-x2x2+x-1=A2x-1+Bx+1 5−x2x2+x−1=A(x+1)+B(2x−1)(2x−1)(x+1)5-x2x2+x-1=A(x+1)+B(2x-1)(2x-1)(x+1)…

• MATH

2×4+8×3+7×2−7x−12×3+4×2+4x2x4+8×3+7×2-7x-12×3+4×2+4x Write the partial fraction decomposition…

You need to decompose the fraction in simple irreducible fractions, such that: 2×4+8×3+7×2−7x−12×3+4×2+4x=2×4+8×3+7×2−7x−12x(x2+4x+4)2×4+8×3+7×2-7x-12×3+4×2+4x=2×4+8×3+7×2-7x-12x(x2+4x+4)

• MATH

x4+2×3+4×2+8x+2×3+2×2+xx4+2×3+4×2+8x+2×3+2×2+x Write the partial fraction decomposition of…

x4+2×3+4×2+8x+2×3+2×2+xx4+2×3+4×2+8x+2×3+2×2+x on long division we get = > (x3+2×2+x)(x3+2×2+x) divides (x4+2×3+4×2+8x+2)(x4+2×3+4×2+8x+2) we get the Quotient’x’′x′ with remainder 3×2+8x+23×2+8x+2…

• MATH

16×4(2x−1)316×4(2x-1)3 Write the partial fraction decomposition of the improper rational…

16×4(2x−1)316×4(2x-1)3 Since the rational expression is an improper expression, we have to express the fraction as a sum of simpler fractions with the degree of the polynomial in the numerator less…

• MATH

x4(x−1)3×4(x-1)3 Write the partial fraction decomposition of the improper rational expression.

First make the substitution x−1=y,x-1=y, or x=y+1.x=y+1. Then the expression becomes (y+1)4y3.(y+1)4y3. Because (y+1)4=y4+4y3+6y2+4y+1,(y+1)4=y4+4y3+6y2+4y+1, the result is y+4+6y+4y2+1y3.y+4+6y+4y2+1y3. Recall y=x−1y=x-1 and…

• MATH

x3+2×2−x+1×2+3x−4×3+2×2-x+1×2+3x-4 Write the partial fraction decomposition of the…

x3+2×2−x+1×2+3x−4×3+2×2-x+1×2+3x-4 Since the rational expression is an improper expression , we have to express the expression as a sum of simpler fractions with the degree of the polynomial in the…

• MATH

2×3−x2+x+5×2+3x+22×3-x2+x+5×2+3x+2 Write the partial fraction decomposition of the…

You need to decompose the fraction in simple irreducible fractions, such that: 2×3−x2+x+5×2+3x+2=2×3−x2+x+5(x+1)(x+2)2×3-x2+x+5×2+3x+2=2×3-x2+x+5(x+1)(x+2)

• MATH

x2−4xx2+x+6×2-4xx2+x+6 Write the partial fraction decomposition of the improper rational…

x2−4xx2+x+6×2-4xx2+x+6 Rewrite the numerator of the rational expression as, x2−4xx2+x+6=x2+x+6−5x−6×2+x+6×2-4xx2+x+6=x2+x+6-5x-6×2+x+6 =(x2+x+6)−(5x+6)x2+x+6=(x2+x+6)-(5x+6)x2+x+6 =1−5x+6×2+x+6=1-5x+6×2+x+6 Polynomials do not…

• MATH

x2−xx2+x+1×2-xx2+x+1 Write the partial fraction decomposition of the improper rational…

x2−xx2+x+1×2-xx2+x+1 Rewrite the rational expression, x2−xx2+x+1=x2+x+1−2x−1×2+x+1×2-xx2+x+1=x2+x+1-2x-1×2+x+1 =(x2+x+1)−(2x+1)x2+x+1=(x2+x+1)-(2x+1)x2+x+1 =1−2x+1×2+x+1=1-2x+1×2+x+1 Polynomials do not completely divide and the…

• MATH

x+1×3(x2+1)2x+1×3(x2+1)2 Write the partial fraction decomposition of the rational…

You need to decompose the fraction in simple irreducible fractions, such that: x+1×3(x2+1)2=Ax+Bx2+Cx3+Dx+Ex2+1+Fx+G(x2+1)2x+1×3(x2+1)2=Ax+Bx2+Cx3+Dx+Ex2+1+Fx+G(x2+1)2 You need to bring to the…

• MATH

8x−12×2(x2+2)28x-12×2(x2+2)2 Write the partial fraction decomposition of the rational…

You need to decompose the fraction in simple irreducible fractions, such that: 8x−12×2(x2+2)2=Ax+Bx2+Cx+Dx2+2+Ex+F(x2+2)28x-12×2(x2+2)2=Ax+Bx2+Cx+Dx2+2+Ex+F(x2+2)2You need to bring to the same…

• MATH

x2−4x+7(x+1)(x2−2x+3)x2-4x+7(x+1)(x2-2x+3) Write the partial fraction decomposition of the…

x2−4x+7(x+1)(x2−2x+3)=Ax+1+Bx+Cx2−2x+3×2-4x+7(x+1)(x2-2x+3)=Ax+1+Bx+Cx2-2x+3 Multiply through by the LCD(x+1)(x2−2x+3)(x+1)(x2-2x+3) x2−4x+7=A(x2−2x+3)+(Bx+C)(x+1)x2-4x+7=A(x2-2x+3)+(Bx+C)(x+1) x2−4x+7=Ax2−2Ax+3A+Bx2+Cx+Bx+Cx2-4x+7=Ax2-2Ax+3A+Bx2+Cx+Bx+C…

• MATH

x2+5(x+1)(x2−2x+3)x2+5(x+1)(x2-2x+3) Write the partial fraction decomposition of the rational…

x2+5(x+1)(x2−2x+3)x2+5(x+1)(x2-2x+3) Letx2+5(x+1)(x2−2x+3)=Ax+1+Bx+Cx2−2x+3×2+5(x+1)(x2-2x+3)=Ax+1+Bx+Cx2-2x+3 x2+5(x+1)(x2−2x+3)=A(x2−2x+3)+(Bx+C)(x+1)(x+1)(x2−2x+3)x2+5(x+1)(x2-2x+3)=A(x2-2x+3)+(Bx+C)(x+1)(x+1)(x2-2x+3)…

• MATH

3×4+x3x4+x Write the partial fraction decomposition of the rational expression. Check…

3×4+x3x4+x Let’s factorize the denominator, x4+x=x(x3+1)x4+x=x(x3+1) =x(x+1)(x2−x+1)=x(x+1)(x2-x+1) Let 3×4+x=Ax+Bx+1+Cx+Dx2−x+13×4+x=Ax+Bx+1+Cx+Dx2-x+1…

• MATH

x16x4−1x16x4-1 Write the partial fraction decomposition of the rational expression. Check…

x16x4−1x16x4-1 Let’s factorize the denominator, 16×4−1=(4×2)2−116×4-1=(4×2)2-1 =(4×2+1)(4×2−1)=(4×2+1)(4×2-1) =(4×2+1)(2x+1)(2x−1)=(4×2+1)(2x+1)(2x-1) Let x16x4−1=A2x+1+B2x−1+Cx+D4x2+1x16x4-1=A2x+1+B2x-1+Cx+D4x2+1…

• MATH

x2x4−2×2−8x2x4-2×2-8 Write the partial fraction decomposition of the rational expression….

x2x4−2×2−8x2x4-2×2-8 Let’s factorize the denominator, x4−2×2−8=x4−4×2+2×2−8×4-2×2-8=x4-4×2+2×2-8 =x2(x2−4)+2(x2−4)=x2(x2-4)+2(x2-4)=(x2+2)(x2−4)=(x2+2)(x2-4) =(x2+2)(x+2)(x−2)=(x2+2)(x+2)(x-2) ∴x2x4−2×2−8=x2(x+2)(x−2)(x2+2)∴x2x4-2×2-8=x2(x+2)(x-2)(x2+2) Let…

• MATH

2×2+x+8(x2+4)22×2+x+8(x2+4)2 Write the partial fraction decomposition of the rational…

2×2+x+8(x2+4)22×2+x+8(x2+4)2 Let2x2+x+8(x2+4)2=Ax+Bx2+4+Cx+D(x2+4)22×2+x+8(x2+4)2=Ax+Bx2+4+Cx+D(x2+4)2 2×2+x+8(x2+4)2=(Ax+B)(x2+4)+Cx+D(x2+4)22×2+x+8(x2+4)2=(Ax+B)(x2+4)+Cx+D(x2+4)2 2×2+x+8(x2+4)2=Ax3+4Ax+Bx2+4B+Cx+D(x2+4)22×2+x+8(x2+4)2=Ax3+4Ax+Bx2+4B+Cx+D(x2+4)2…

• MATH

x+6×3−3×2−4x+12x+6×3-3×2-4x+12 Write the partial fraction decomposition of the rational…

x+6×3−3×2−4x+12x+6×3-3×2-4x+12 To decompose this to partial fractions, factor the denominator. x3−3×2−4x+12×3-3×2-4x+12 =(x3−3×2)+(−4x+12)=(x3-3×2)+(-4x+12) =x2(x−3)−4(x−3)=x2(x-3)-4(x-3) =(x−3)(x2−4)=(x-3)(x2-4) =(x−3)(x−2)(x+2)=(x-3)(x-2)(x+2)…

• MATH

xx3−x2−2x+2xx3-x2-2x+2 Write the partial fraction decomposition of the rational…

Decompose the denominator: x3−x2−2x+2=x2(x−1)−2(x−1)=(x2−2)(x−1)=(x−1)(x−2–√)(x+2–√).x3-x2-2x+2=x2(x-1)-2(x-1)=(x2-2)(x-1)=(x-1)(x-2)(x+2).Therefore the fraction decomposition has the form…

• MATH

2xx3−12xx3-1 Write the partial fraction decomposition of the rational expression. Check…

The denominator factors out as x3−1=(x−1)(x2+x+1),x3-1=(x-1)(x2+x+1),thus the general decomposition is 2xx3−1=Ax−1+Bx+Cx2+x+1.2xx3-1=Ax-1+Bx+Cx2+x+1. To find A, B and C, multiply both sides by x3−1:x3-1:

• MATH

x2+2x+8(x2+4)2×2+2x+8(x2+4)2 Write the partial fraction decomposition of the rational…

x2+2x+8(x2+4)2=x2+2x+8(x2+4)(x2+4)x2+2x+8(x2+4)2=x2+2x+8(x2+4)(x2+4) x2+2x+8(x2+4)2=Ax+Bx2+4+Cx+D(x2+4)2×2+2x+8(x2+4)2=Ax+Bx2+4+Cx+D(x2+4)2 Multiply through by the LCD (x2+4)2.(x2+4)2. x2+2x+8=(Ax+B)(x2+4)+(Cx+D)x2+2x+8=(Ax+B)(x2+4)+(Cx+D)…