Simplify (1-4/(x+8))/(16/(x+8)+x)

$\frac{1 - \frac{4}{x + 8}}{\frac{16}{x + 8} + x}$

Step 1

Multiply the numerator and denominator of the complex fraction by $x + 8$ .

Multiply $\frac{1 - \frac{4}{x + 8}}{\frac{16}{x + 8} + x}$ by $\frac{x + 8}{x + 8}$ .

$\frac{x + 8}{x + 8} \cdot \frac{1 - \frac{4}{x + 8}}{\frac{16}{x + 8} + x}$

Combine.

$\frac{(x + 8) (1 - \frac{4}{x + 8})}{(x + 8) (\frac{16}{x + 8} + x)}$

Step 2

Apply the distributive property.

$\frac{(x + 8) \cdot 1 + (x + 8) (- \frac{4}{x + 8})}{(x + 8) \frac{16}{x + 8} + (x + 8) x}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x + 8$ .

Move the leading negative in $- \frac{4}{x + 8}$ into the numerator.

$\frac{(x + 8) \cdot 1 + (x + 8) \frac{- 4}{x + 8}}{(x + 8) \frac{16}{x + 8} + (x + 8) x}$

Cancel the common factor.

$\frac{(x + 8) \cdot 1 + (x + 8) \frac{- 4}{x + 8}}{(x + 8) \frac{16}{x + 8} + (x + 8) x}$

Rewrite the expression.

$\frac{(x + 8) \cdot 1 - 4}{(x + 8) \frac{16}{x + 8} + (x + 8) x}$

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{(x + 8) \cdot 1 - 4}{(x + 8) \frac{16}{x + 8} + (x + 8) x}$

Rewrite the expression.

$\frac{(x + 8) \cdot 1 - 4}{16 + (x + 8) x}$

Step 4

Simplify the numerator.

Multiply $x + 8$ by $1$ .

$\frac{x + 8 - 4}{16 + (x + 8) x}$

Subtract $4$ from $8$ .

$\frac{x + 4}{16 + (x + 8) x}$

Step 5

Simplify the denominator.

Apply the distributive property.

$\frac{x + 4}{16 + x \cdot x + 8 x}$

Multiply $x$ by $x$ .

$\frac{x + 4}{16 + x^{2} + 8 x}$

Reorder terms.

$\frac{x + 4}{x^{2} + 8 x + 16}$

Factor using the perfect square rule.

Rewrite $16$ as $4^{2}$ .

$\frac{x + 4}{x^{2} + 8 x + 4^{2}}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x = 2 \cdot x \cdot 4$

Rewrite the polynomial.

$\frac{x + 4}{x^{2} + 2 \cdot x \cdot 4 + 4^{2}}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 4$ .

$\frac{x + 4}{{(x + 4)}^{2}}$

Step 6

Cancel the common factor of $x + 4$ and ${(x + 4)}^{2}$ .

Multiply by $1$ .

$\frac{(x + 4) \cdot 1}{{(x + 4)}^{2}}$

Cancel the common factors.

Factor $x + 4$ out of ${(x + 4)}^{2}$ .

$\frac{(x + 4) \cdot 1}{(x + 4) (x + 4)}$

Cancel the common factor.

$\frac{(x + 4) \cdot 1}{(x + 4) (x + 4)}$

Rewrite the expression.

$\frac{1}{x + 4}$

Simplify (1-4/(x+8))/(16/(x+8)+x)

Related Questions

Support LCMGCF.com by disabling your adblocker.