Answer
$\dfrac{\dfrac{1}{5}-\dfrac{1}{x}}{\dfrac{7}{10}+\dfrac{1}{x^{2}}}=\dfrac{2x(x-5)}{7x^{2}+10}$
Work Step by Step
$\dfrac{\dfrac{1}{5}-\dfrac{1}{x}}{\dfrac{7}{10}+\dfrac{1}{x^{2}}}$
Evaluate the substraction indicated in the numerator and the sum indicated in the denominator:
$\dfrac{\dfrac{1}{5}-\dfrac{1}{x}}{\dfrac{7}{10}+\dfrac{1}{x^{2}}}=\dfrac{\dfrac{x-5}{5x}}{\dfrac{7x^{2}+10}{10x^{2}}}=...$
Evaluate the division and simplify if possible:
$...=\dfrac{x-5}{5x}\div\dfrac{7x^{2}+10}{10x^{2}}=\dfrac{(x-5)(10x^{2})}{(7x^{2}+10)(5x)}=...$
$...=\dfrac{(x-5)(2x)}{7x^{2}+10}=\dfrac{2x(x-5)}{7x^{2}+10}$
