How do you express $(x + 2)/((2x+7)(x+1))$ in partial fractions?

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Answer 1 · 2016-11-12T02:41:24

$A/(2x+ 7) + B/(x + 1) = (x+ 2)/((2x + 7)(x + 1))$

Put on a common denominator.

$(A(x + 1))/((2x+ 7)(x + 1)) + (B(2x + 7))/((2x + 7)(x + 1)) = (x+2)/((2x+ 7)(x + 1))$

$Ax + A + 2Bx + 7B = x+ 2$

$(A + 2B)x + (A + 7B) = x + 2$

So, $A + 2B = 1$ and $A + 7B = 2$ .

Solve.

$A = 1 - 2B -> 1 - 2B + 7B = 2$

$5B = 1$

$B = 1/5$

$:.A = 1 - 2(1/5) = 3/5$

Hence, the partial fraction decomposition is $3/(5(2x + 7)) + 1/(5(x+ 1)) = (x + 2)/((2x + 7)(x + 1))$ .

Hopefully this helps!

How do you express (x + 2)/((2x+7)(x+1)) (x + 2)/((2x+7)(x+1)) in partial fractions?