What is (3/(x+h)-3/x)/h ?

The solution to (3/(x+h)-3/x)/h is -3/(x(x+h))

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simplify (3/(x+h)-3/x)/h

simplify

\frac{\frac{3}{x + h} - \frac{3}{x}}{h}

- \frac{3}{x ( x + h )}

Solution steps

\frac{\frac{3}{x + h} - \frac{3}{x}}{h}

Join

\frac{3}{x + h} - \frac{3}{x} : - \frac{3 h}{x ( x + h )}

= \frac{- \frac{3 h}{x ( x + h )}}{h}

Apply the fraction rule:

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

= - \frac{\frac{3 h}{x ( x + h )}}{h}

Apply the fraction rule:

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

\frac{\frac{3 h}{x ( x + h )}}{h} = \frac{3 h}{x ( x + h ) h}

= - \frac{3 h}{x ( x + h ) h}

Cancel the common factor:

h

= - \frac{3}{x ( x + h )}

2 x^{2} + 5 x + 3 = 0

(7 x)^{3}

27 + 4.5 x \geq 81

7 - \frac{3}{x} > 4

8 \cdot 0.25