Simplify (x-4/x)/((x+5)/6+1/x)

$\frac{x - \frac{4}{x}}{\frac{x + 5}{6} + \frac{1}{x}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $x \cdot 6$ .

Multiply $\frac{x - \frac{4}{x}}{\frac{x + 5}{6} + \frac{1}{x}}$ by $\frac{x \cdot 6}{x \cdot 6}$ .

$\frac{x \cdot 6}{x \cdot 6} \cdot \frac{x - \frac{4}{x}}{\frac{x + 5}{6} + \frac{1}{x}}$

Combine.

$\frac{x \cdot 6 (x - \frac{4}{x})}{x \cdot 6 (\frac{x + 5}{6} + \frac{1}{x})}$

Step 2

Apply the distributive property.

$\frac{x \cdot 6 x + x \cdot 6 (- \frac{4}{x})}{x \cdot 6 \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{4}{x}$ into the numerator.

$\frac{x \cdot 6 x + x \cdot 6 \frac{- 4}{x}}{x \cdot 6 \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Factor $x$ out of $x \cdot 6$ .

$\frac{x \cdot 6 x + x (6) \frac{- 4}{x}}{x \cdot 6 \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Cancel the common factor.

$\frac{x \cdot 6 x + x \cdot 6 \frac{- 4}{x}}{x \cdot 6 \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Rewrite the expression.

$\frac{x \cdot 6 x + 6 \cdot - 4}{x \cdot 6 \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Multiply $6$ by $- 4$ .

$\frac{x \cdot 6 x - 24}{x \cdot 6 \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Cancel the common factor of $6$ .

Factor $6$ out of $x \cdot 6$ .

$\frac{x \cdot 6 x - 24}{6 \cdot x \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Cancel the common factor.

$\frac{x \cdot 6 x - 24}{6 \cdot x \frac{x + 5}{6} + x \cdot 6 \frac{1}{x}}$

Rewrite the expression.

$\frac{x \cdot 6 x - 24}{x (x + 5) + x \cdot 6 \frac{1}{x}}$

Cancel the common factor of $x$ .

Factor $x$ out of $x \cdot 6$ .

$\frac{x \cdot 6 x - 24}{x (x + 5) + x (6) \frac{1}{x}}$

Cancel the common factor.

$\frac{x \cdot 6 x - 24}{x (x + 5) + x \cdot 6 \frac{1}{x}}$

Rewrite the expression.

$\frac{x \cdot 6 x - 24}{x (x + 5) + 6}$

Step 4

Simplify the numerator.

Factor $6$ out of $x \cdot 6 x - 24$ .

Factor $6$ out of $x \cdot 6 x$ .

$\frac{6 (x \cdot x) - 24}{x (x + 5) + 6}$

Factor $6$ out of $- 24$ .

$\frac{6 (x \cdot x) + 6 \cdot - 4}{x (x + 5) + 6}$

Factor $6$ out of $6 (x \cdot x) + 6 \cdot - 4$ .

$\frac{6 (x \cdot x - 4)}{x (x + 5) + 6}$

Raise $x$ to the power of $1$ .

$\frac{6 (x^{1} x - 4)}{x (x + 5) + 6}$

Raise $x$ to the power of $1$ .

$\frac{6 (x^{1} x^{1} - 4)}{x (x + 5) + 6}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 (x^{1 + 1} - 4)}{x (x + 5) + 6}$

Add $1$ and $1$ .

$\frac{6 (x^{2} - 4)}{x (x + 5) + 6}$

Rewrite $4$ as $2^{2}$ .

$\frac{6 (x^{2} - 2^{2})}{x (x + 5) + 6}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$\frac{6 (x + 2) (x - 2)}{x (x + 5) + 6}$

Step 5

Simplify the denominator.

Apply the distributive property.

$\frac{6 (x + 2) (x - 2)}{x \cdot x + x \cdot 5 + 6}$

Multiply $x$ by $x$ .

$\frac{6 (x + 2) (x - 2)}{x^{2} + x \cdot 5 + 6}$

Move $5$ to the left of $x$ .

$\frac{6 (x + 2) (x - 2)}{x^{2} + 5 \cdot x + 6}$

Factor $x^{2} + 5 x + 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $6$ and whose sum is $5$ .

$2, 3$

Write the factored form using these integers.

$\frac{6 (x + 2) (x - 2)}{(x + 2) (x + 3)}$

Step 6

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{6 (x + 2) (x - 2)}{(x + 2) (x + 3)}$

Rewrite the expression.

$\frac{6 (x - 2)}{x + 3}$

Simplify (x-4/x)/((x+5)/6+1/x)

Related Questions

Support LCMGCF.com by disabling your adblocker.