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notsponge [240]
3 years ago
8

I need help with this math problem

Mathematics
1 answer:
den301095 [7]3 years ago
8 0

Answer:

1). \frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}

2). \frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}

Step-by-step explanation:

In this question we have to write the fractions in the factored form.

Rational expressions are \frac{2}{x^{2}-x-12 } and \frac{1}{x^{2}-16 }.

1). \frac{2}{x^{2}-x-12 }

Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12

                                                                           = x(x - 4) + 3(x - 4)

                                                                           = (x + 3)(x - 4)

Therefore. \frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}

2). \frac{1}{x^{2}-16 }

Factored form of the denominator (x² - 16) = (x - 4)(x + 4)

[Since (a²- b²) = (a - b)(a + b)]

Therefore, \frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}

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