What is (x+1)/x-x/(x+1) ?

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

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simplify (x+1)/x-x/(x+1)

simplify

\frac{x + 1}{x} - \frac{x}{x + 1}

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

Solution steps

\frac{x + 1}{x} - \frac{x}{x + 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

(3 x - 6 y)^{2}

8 147 x - 3 48 x

6 x^{4} - 16 x^{3} - 84 x^{2} + 82 x + 60

2 \frac{1}{3} + 1 \frac{5}{9}

\frac{9 x - 6}{3}