Find f(g(x)) f(x)=(x-5)/(x+8) g(x)=(x+4)/(x-7)

$f (x) = \frac{x - 5}{x + 8}$ $g (x) = \frac{x + 4}{x - 7}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 4}{x - 7})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 4}{x - 7}) = \frac{(\frac{x + 4}{x - 7}) - 5}{(\frac{x + 4}{x - 7}) + 8}$

Step 3

Multiply the numerator and denominator of the complex fraction by $x - 7$ .

Multiply $\frac{\frac{x + 4}{x - 7} - 5}{\frac{x + 4}{x - 7} + 8}$ by $\frac{x - 7}{x - 7}$ .

$f (\frac{x + 4}{x - 7}) = \frac{x - 7}{x - 7} \cdot \frac{\frac{x + 4}{x - 7} - 5}{\frac{x + 4}{x - 7} + 8}$

Combine.

$f (\frac{x + 4}{x - 7}) = \frac{(x - 7) (\frac{x + 4}{x - 7} - 5)}{(x - 7) (\frac{x + 4}{x - 7} + 8)}$

Step 4

Apply the distributive property.

$f (\frac{x + 4}{x - 7}) = \frac{(x - 7) (\frac{x + 4}{x - 7}) + (x - 7) \cdot - 5}{(x - 7) (\frac{x + 4}{x - 7}) + (x - 7) \cdot 8}$

Step 5

Simplify by cancelling.

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$f (\frac{x + 4}{x - 7}) = \frac{(x - 7) (\frac{x + 4}{x - 7}) + (x - 7) \cdot - 5}{(x - 7) (\frac{x + 4}{x - 7}) + (x - 7) \cdot 8}$

Rewrite the expression.

$f (\frac{x + 4}{x - 7}) = \frac{x + 4 + (x - 7) \cdot - 5}{(x - 7) (\frac{x + 4}{x - 7}) + (x - 7) \cdot 8}$

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$f (\frac{x + 4}{x - 7}) = \frac{x + 4 + (x - 7) \cdot - 5}{(x - 7) (\frac{x + 4}{x - 7}) + (x - 7) \cdot 8}$

Rewrite the expression.

$f (\frac{x + 4}{x - 7}) = \frac{x + 4 + (x - 7) \cdot - 5}{x + 4 + (x - 7) \cdot 8}$

Step 6

Simplify the numerator.

Apply the distributive property.

$f (\frac{x + 4}{x - 7}) = \frac{x + 4 + x \cdot - 5 - 7 \cdot - 5}{x + 4 + (x - 7) \cdot 8}$

Move $- 5$ to the left of $x$ .

$f (\frac{x + 4}{x - 7}) = \frac{x + 4 - 5 \cdot x - 7 \cdot - 5}{x + 4 + (x - 7) \cdot 8}$

Multiply $- 7$ by $- 5$ .

$f (\frac{x + 4}{x - 7}) = \frac{x + 4 - 5 \cdot x + 35}{x + 4 + (x - 7) \cdot 8}$

Subtract $5 x$ from $x$ .

$f (\frac{x + 4}{x - 7}) = \frac{- 4 x + 4 + 35}{x + 4 + (x - 7) \cdot 8}$

Add $4$ and $35$ .

$f (\frac{x + 4}{x - 7}) = \frac{- 4 x + 39}{x + 4 + (x - 7) \cdot 8}$

Step 7

Simplify the denominator.

Apply the distributive property.

$f (\frac{x + 4}{x - 7}) = \frac{- 4 x + 39}{x + 4 + x \cdot 8 - 7 \cdot 8}$

Move $8$ to the left of $x$ .

$f (\frac{x + 4}{x - 7}) = \frac{- 4 x + 39}{x + 4 + 8 \cdot x - 7 \cdot 8}$

Multiply $- 7$ by $8$ .

$f (\frac{x + 4}{x - 7}) = \frac{- 4 x + 39}{x + 4 + 8 \cdot x - 56}$

Add $x$ and $8 x$ .

$f (\frac{x + 4}{x - 7}) = \frac{- 4 x + 39}{9 x + 4 - 56}$

Subtract $56$ from $4$ .

$f (\frac{x + 4}{x - 7}) = \frac{- 4 x + 39}{9 x - 52}$

Step 8

Simplify with factoring out.

Factor $- 1$ out of $- 4 x$ .

$f (\frac{x + 4}{x - 7}) = \frac{- (4 x) + 39}{9 x - 52}$

Rewrite $39$ as $- 1 (- 39)$ .

$f (\frac{x + 4}{x - 7}) = \frac{- (4 x) - 1 \cdot - 39}{9 x - 52}$

Factor $- 1$ out of $- (4 x) - 1 (- 39)$ .

$f (\frac{x + 4}{x - 7}) = \frac{- (4 x - 39)}{9 x - 52}$

Simplify the expression.

Rewrite $- (4 x - 39)$ as $- 1 (4 x - 39)$ .

$f (\frac{x + 4}{x - 7}) = \frac{- 1 (4 x - 39)}{9 x - 52}$

Move the negative in front of the fraction.

$f (\frac{x + 4}{x - 7}) = - \frac{4 x - 39}{9 x - 52}$

Find f(g(x)) f(x)=(x-5)/(x+8) g(x)=(x+4)/(x-7)

Related Questions

Support LCMGCF.com by disabling your adblocker.