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What two rational expressions sum to 2x-2/x^2-x-12

Dec 6, 2022

#1
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I guess this should look like:  $$\frac{2x-2}{x^2-x-12}$$

If so, it can be written as $$\frac{2x-2}{(x-4)(x+3)}$$

Express as partial fractions:  $$\frac{2x-2}{(x-4)(x+3)} = \frac{A}{x-4}+\frac{B}{x+3}$$

from which we find

$$A + B = 2\\\\3A-4B=-2$$

i'll leave you to find A and B.

Dec 6, 2022