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Mazyrski [523]
2 years ago
12

Not good with factoring could use a hand.

Mathematics
1 answer:
MrRa [10]2 years ago
6 0

The only factoring you need to do is already done for you:

<em>x</em>² + <em>x</em> - 12 = (<em>x</em> + 4) (<em>x</em> - 3)

What you're asked to do is decompose

(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12)

into partial fractions, i.e. find <em>a</em> and <em>b</em> such that

(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = <em>a</em> / (<em>x</em> + 4) + <em>b</em> / (<em>x</em> - 3)

Multiply both sides by <em>x</em>² + <em>x</em> - 12 :

3<em>x</em> - 4 = <em>a</em> (<em>x</em> - 3) + <em>b</em> (<em>x</em> + 4)

3<em>x</em> - 4 = (<em>a</em> + <em>b</em>) <em>x</em> + (-3<em>a</em> + 4<em>b</em>)

So we have

<em>a</em> + <em>b</em> = 3

-3<em>a</em> + 4<em>b</em> = -4

and solving this system gives

<em>a</em> = 16/7 and <em>b</em> = 5/7

so you should submit the numbers in bold:

(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = 16 / (7 (<em>x</em> + 4)) + 5 / (7 (<em>x</em> - 3))

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