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Anettt [7]
3 years ago
10

F(x)=3x2+10x-25 g(x)=9x2-25 Find (f/g)(x).

Mathematics
1 answer:
son4ous [18]3 years ago
5 0

Answer:

(f/g)(x) =  \frac{x + 5}{3x + 5}

Step-by-step explanation:

f(x) = 3x² + 10x - 25

g(x) = 9x² - 25

To find (f/g)(x) divide f(x) by g(x)

That's

(f/g)(x) =  \frac{3 {x}^{2} + 10x - 25 }{9 {x}^{2} - 25 }

Factorize both the numerator and the denominator

<u>For the numerator</u>

3x² + 10x - 25

3x² + 15x - 5x - 25

3x ( x + 5) - 5( x + 5)

(3x - 5 ) ( x + 5)

<u>For the denominator</u>

9x² - 25

(3x)² - 5²

Using the formula

a² - b² = ( a + b)(a - b)

(3x)² - 5² = (3x + 5)(3x - 5)

So we have

(f/g)(x) =  \frac{(3x - 5)(x + 5)}{(3x + 5)(3x - 5)}

Simplify

We have the final answer as

(f/g)(x) =  \frac{x + 5}{3x + 5}

Hope this helps you

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