Simplify (20/x-25/(2x))/(5/(x^2)+1/8)

$\frac{\frac{20}{x} - \frac{25}{2 x}}{\frac{5}{x^{2}} + \frac{1}{8}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $8 x^{2}$ .

Multiply $\frac{\frac{20}{x} - \frac{25}{2 x}}{\frac{5}{x^{2}} + \frac{1}{8}}$ by $\frac{8 x^{2}}{8 x^{2}}$ .

$\frac{8 x^{2}}{8 x^{2}} \cdot \frac{\frac{20}{x} - \frac{25}{2 x}}{\frac{5}{x^{2}} + \frac{1}{8}}$

Combine.

$\frac{8 x^{2} (\frac{20}{x} - \frac{25}{2 x})}{8 x^{2} (\frac{5}{x^{2}} + \frac{1}{8})}$

Step 2

Apply the distributive property.

$\frac{8 x^{2} \frac{20}{x} + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Factor $x$ out of $8 x^{2}$ .

$\frac{x (8 x) \frac{20}{x} + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Cancel the common factor.

$\frac{x (8 x) \frac{20}{x} + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Rewrite the expression.

$\frac{8 x \cdot 20 + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Multiply $20$ by $8$ .

$\frac{160 x + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Cancel the common factor of $2 x$ .

Move the leading negative in $- \frac{25}{2 x}$ into the numerator.

$\frac{160 x + 8 x^{2} \frac{- 25}{2 x}}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Factor $2 x$ out of $8 x^{2}$ .

$\frac{160 x + 2 x (4 x) \frac{- 25}{2 x}}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Cancel the common factor.

$\frac{160 x + 2 x (4 x) \frac{- 25}{2 x}}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Rewrite the expression.

$\frac{160 x + 4 x \cdot - 25}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Multiply $- 25$ by $4$ .

$\frac{160 x - 100 x}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Cancel the common factor of $x^{2}$ .

Factor $x^{2}$ out of $8 x^{2}$ .

$\frac{160 x - 100 x}{x^{2} \cdot 8 \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Cancel the common factor.

$\frac{160 x - 100 x}{x^{2} \cdot 8 \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Rewrite the expression.

$\frac{160 x - 100 x}{8 \cdot 5 + 8 x^{2} \frac{1}{8}}$

Multiply $8$ by $5$ .

$\frac{160 x - 100 x}{40 + 8 x^{2} \frac{1}{8}}$

Cancel the common factor of $8$ .

Factor $8$ out of $8 x^{2}$ .

$\frac{160 x - 100 x}{40 + 8 (x^{2}) \frac{1}{8}}$

Cancel the common factor.

$\frac{160 x - 100 x}{40 + 8 x^{2} \frac{1}{8}}$

Rewrite the expression.

$\frac{160 x - 100 x}{40 + x^{2}}$

Step 4

Subtract $100 x$ from $160 x$ .

$\frac{60 x}{40 + x^{2}}$

Simplify (20/x-25/(2x))/(5/(x^2)+1/8)

Related Questions

Support LCMGCF.com by disabling your adblocker.