Question

Add the given expressions, simplifying each result and noting the combined excluded values.

Answer 1

Answer:

The sum of the given expressions is $\frac{(2+x)(8-x)}{x(x+4)}$

x = 0 and x = -4

Step-by-step explanation:

we need to find the sum of the given expressions

$\frac{6}{4+x} +\frac{4-x}{x} \\= \frac{6*x+(4-x)(4+x)}{(4+x)*x} \\=\frac{6x+16-x^2}{x(x+4)} \\=\frac{16+6x-x^2}{x(x+4)} \\=\frac{(2+x)(8-x)}{x(x+4)}$

To find excluded values:

x ( 4 + x ) = 0

x = 0  and 4 + x = 0

∴ x = 0 and x = -4