Question

4x² -3y² in fraction form​

Answer 1

Answer:

First, we’ll factor denominator. Since x=−1 is an obvious root, then (x+1) is a factor. We can then use polynomial long division or synthetic division to find the quadratic factor:

−11↓1−4−1−51566−60

x3−4x2+x+6=(x+1)(x2−5x+6)=(x+1)(x−2)(x−3)

Set up partial fraction:

5x2−14x−10x3−4x2+x+6=5x2−14x−10(x+1)(x−2)(x−3)=Ax+1+Bx−2+Cx−3

Multiply both sides by least common denominator:

5x2−14x−10=(x−2)(x−3)A+(x+1)(x−3)B+(x+1)(x−2)C

Let x=−1

5(−1)2−14(−1)−10=(−1−2)(−1−3)A+0B+0C

9=12A⟹A=34

Let x=2

5(2)2−14(2)−10=0A+(2+1)(2−3)B+0C

Step-by-step explanation:

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