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Rus_ich [418]
3 years ago
7

What two rational expressions sum to

mula1" title="\frac{4x+2}{x^{2}-9+8 }" alt="\frac{4x+2}{x^{2}-9+8 }" align="absmiddle" class="latex-formula"> Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.

Mathematics
2 answers:
Darina [25.2K]3 years ago
8 0

Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)

bulgar [2K]3 years ago
3 0

Answer:

\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}

Step-by-step explanation:

Given

\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}

Required

Fill in the gaps

Going by the given parameters, we have that

\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}

x^2 - 9x + 8, when factorized is (x-1)(x-8)

Hence; the expression becomes

\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}

Combine Fractions

\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}

Simplify the denominators

4x + 2 = A + B

By direct comparison

A = 4x

B = 2

Hence, the complete expression is

\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}

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