What is expand (11)/(8(x-4))+5/(8(x+4)) ?

The solution to expand (11)/(8(x-4))+5/(8(x+4)) is (2x+3)/(x^2-16)

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expand (11)/(8(x-4))+5/(8(x+4))

expand

\frac{11}{8 ( x - 4 )} + \frac{5}{8 ( x + 4 )}

\frac{2 x + 3}{x ^{2} - 16}

Solution steps

\frac{11}{8 ( x - 4 )} + \frac{5}{8 ( x + 4 )}

Expand

8 (x - 4) : 8 x - 32

= \frac{11}{8 x - 32} + \frac{5}{8 ( x + 4 )}

Expand

8 (x + 4) : 8 x + 32

= \frac{11}{8 x - 32} + \frac{5}{8 x + 32}

Factor

8 x - 32 : 8 (x - 4)

= \frac{11}{8 ( x - 4 )} + \frac{5}{8 x + 32}

Factor

8 x + 32 : 8 (x + 4)

= \frac{11}{8 ( x - 4 )} + \frac{5}{8 ( x + 4 )}

Least Common Multiplier of

8 (x - 4), 8 (x + 4) : 8 (x - 4) (x + 4)

Adjust Fractions based on the LCM

= \frac{11 ( x + 4 )}{8 ( x - 4 ) ( x + 4 )} + \frac{5 ( x - 4 )}{8 ( x + 4 ) ( x - 4 )}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{11 ( x + 4 ) + 5 ( x - 4 )}{8 ( x - 4 ) ( x + 4 )}

Factor

11 (x + 4) + 5 (x - 4) : 8 (2 x + 3)

= \frac{8 ( 2 x + 3 )}{8 ( x - 4 ) ( x + 4 )}

Divide the numbers:

\frac{8}{8} = 1

= \frac{2 x + 3}{( x - 4 ) ( x + 4 )}

Expand

(x - 4) (x + 4) : x^{2} - 16

= \frac{2 x + 3}{x ^{2} - 16}

\frac{4 x ^{2}}{( 1 - x ^{2} ) ^{2}}

\frac{( ( L + d - x ) ^{2} - x )}{( ( ( L + d - x ) ^{2} - x ) ^{2} + h ^{2} )}

\frac{1}{( s + 1 ) ^{2} \cdot ( s - 2 )}

\frac{6 ( x + 2 )}{( x + 1 ) ( x + 3 ) ( x + 4 )}

\frac{s ^{2} + 2 s - k}{( s ^{2} + k ) ( s - k )}

What is expand (11)/(8(x-4))+5/(8(x+4)) ?
The solution to expand (11)/(8(x-4))+5/(8(x+4)) is (2x+3)/(x^2-16)