Simplify (1/(4p)-3/p)/(1/(4p)+4/p)

$\frac{\frac{1}{4 p} - \frac{3}{p}}{\frac{1}{4 p} + \frac{4}{p}}$

Multiply the numerator and denominator of the complex fraction by $4 p$ .

Multiply $\frac{\frac{1}{4 p} - \frac{3}{p}}{\frac{1}{4 p} + \frac{4}{p}}$ by $\frac{4 p}{4 p}$ .

$\frac{4 p}{4 p} \cdot \frac{\frac{1}{4 p} - \frac{3}{p}}{\frac{1}{4 p} + \frac{4}{p}}$

Combine.

$\frac{4 p (\frac{1}{4 p} - \frac{3}{p})}{4 p (\frac{1}{4 p} + \frac{4}{p})}$

Apply the distributive property.

$\frac{4 p \frac{1}{4 p} + 4 p (- \frac{3}{p})}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Simplify by cancelling.

Cancel the common factor of $4 p$ .

Cancel the common factor.

$\frac{4 p \frac{1}{4 p} + 4 p (- \frac{3}{p})}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Rewrite the expression.

$\frac{1 + 4 p (- \frac{3}{p})}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Cancel the common factor of $p$ .

Move the leading negative in $- \frac{3}{p}$ into the numerator.

$\frac{1 + 4 p \frac{- 3}{p}}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Factor $p$ out of $4 p$ .

$\frac{1 + p \cdot 4 \frac{- 3}{p}}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Cancel the common factor.

$\frac{1 + p \cdot 4 \frac{- 3}{p}}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Rewrite the expression.

$\frac{1 + 4 \cdot - 3}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Multiply $4$ by $- 3$ .

$\frac{1 - 12}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Cancel the common factor of $4 p$ .

Cancel the common factor.

$\frac{1 - 12}{4 p \frac{1}{4 p} + 4 p \frac{4}{p}}$

Rewrite the expression.

$\frac{1 - 12}{1 + 4 p \frac{4}{p}}$

Cancel the common factor of $p$ .

Factor $p$ out of $4 p$ .

$\frac{1 - 12}{1 + p \cdot 4 \frac{4}{p}}$

Cancel the common factor.

$\frac{1 - 12}{1 + p \cdot 4 \frac{4}{p}}$

Rewrite the expression.

$\frac{1 - 12}{1 + 4 \cdot 4}$

Multiply $4$ by $4$ .

$\frac{1 - 12}{1 + 16}$

Simplify the expression.

Subtract $12$ from $1$ .

$\frac{- 11}{1 + 16}$

Add $1$ and $16$ .

$\frac{- 11}{17}$

Move the negative in front of the fraction.

$- \frac{11}{17}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{11}{17}$

Decimal Form:

$- 0.64705882 \dots$

Simplify (1/(4p)-3/p)/(1/(4p)+4/p)

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