What is expand 1/x+1/(x+7)+1/(x+1) ?

The solution to expand 1/x+1/(x+7)+1/(x+1) is (3x^2+16x+7)/(x^3+8x^2+7x)

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expand 1/x+1/(x+7)+1/(x+1)

expand

\frac{1}{x} + \frac{1}{x + 7} + \frac{1}{x + 1}

\frac{3 x ^{2} + 16 x + 7}{x ^{3} + 8 x ^{2} + 7 x}

Solution steps

\frac{1}{x} + \frac{1}{x + 7} + \frac{1}{x + 1}

Least Common Multiplier of

x, x + 7, x + 1 : x (x + 7) (x + 1)

Adjust Fractions based on the LCM

= \frac{( x + 7 ) ( x + 1 )}{x ( x + 7 ) ( x + 1 )} + \frac{x ( x + 1 )}{x ( x + 7 ) ( x + 1 )} + \frac{x ( x + 7 )}{x ( x + 7 ) ( x + 1 )}

Since the denominators are equal, combine the fractions:

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

= \frac{( x + 7 ) ( x + 1 ) + x ( x + 1 ) + x ( x + 7 )}{x ( x + 7 ) ( x + 1 )}

Expand

x (x + 7) (x + 1) : x^{3} + 8 x^{2} + 7 x

= \frac{( x + 7 ) ( x + 1 ) + x ( x + 1 ) + x ( x + 7 )}{x ^{3} + 8 x ^{2} + 7 x}

Expand

(x + 7) (x + 1) + x (x + 1) + x (x + 7) : 3 x^{2} + 16 x + 7

= \frac{3 x ^{2} + 16 x + 7}{x ^{3} + 8 x ^{2} + 7 x}

\frac{x ^{2} + 2}{x ( x - 2 )}

\frac{1}{w ( w + i ) ^{2}}

(z + Δ z)^{2}

- \frac{7 ( 3 + 3 )}{6}

What is expand 1/x+1/(x+7)+1/(x+1) ?
The solution to expand 1/x+1/(x+7)+1/(x+1) is (3x^2+16x+7)/(x^3+8x^2+7x)