Question

reduce the rational expressions x²-16÷x²+8x+16 to its lowest form ​

Answer 1

Answer:

Step

1. ($x^2-16$)/(x²+8x+16)

($x^2-16$)= $x^2 - 4^2$ = (x - 4)(x + 4)

$x^2+8x +16=$$x^2+4x+4x+16 =x(x+4)+4(x+4)=(x+4)(x+4)$

∴x²-16÷x²+8x+16=(x-4)(x+4)/(x+4)(x+4)

                           =(x-4)/(x+4)

Answer 2

The lowest form is $\frac{x}{8} - \frac{2}{8} - \frac{3}{2x} - \frac{3}{4}$.

Given

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

To Find

Lowest reduced form

Solution

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

$= \frac{x^2 - 4-12}{8x + 16}$

$= \frac{x^2 - 2^2-12}{8x + 16}$

We know that a² - b² = (a  + b)(a - b)

Therefore, the expression is

= $\frac{(x + 2)(x-2)}{8x + 16} - \frac{12}{8x+16}$

Now taking 8 common in the denominator we get

$\frac{(x + 2)(x-2)}{8(x + 2)} - \frac{3}{2(x+2)}$

Now canceling (x +2) out of the numerator and denominator we get

$\frac{(x-2)}{8} - \frac{3}{2(x+2)}$

$= \frac{x}{8} - \frac{2}{8} - \frac{3}{2x} - \frac{3}{4}$

Adding the constants up we get

$\frac{x}{8} - \frac{3}{2x} - \frac{5}{4}$

$\frac{x}{8} - \frac{2}{8} - \frac{3}{2x} - \frac{3}{4}$

Therefore the lowest form is $\frac{x}{8} - \frac{2}{8} - \frac{3}{2x} - \frac{3}{4}$.

#SPJ2