What is 1/(x^2)+1/(x^2+x) ?

The solution to 1/(x^2)+1/(x^2+x) is (2x+1)/(x^2(x+1))

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simplify 1/(x^2)+1/(x^2+x)

simplify

\frac{1}{x ^{2}} + \frac{1}{x ^{2} + x}

\frac{2 x + 1}{x ^{2} ( x + 1 )}

Solution steps

\frac{1}{x ^{2}} + \frac{1}{x ^{2} + x}

Least Common Multiplier of

x^{2}, x^{2} + x : x^{2} (x + 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x + 1 + x : 2 x + 1

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

\frac{a}{b} \cdot \frac{b}{a}

2 x \cdot 4 x^{2}

a - (x + y) - 3 (x - y) + 2 [- (x - 2 y) - 2 (- x - y)]

x^{2} \cdot 4 x

- 6 + 4 q + (- 6 q)

What is 1/(x^2)+1/(x^2+x) ?
The solution to 1/(x^2)+1/(x^2+x) is (2x+1)/(x^2(x+1))