Algebra Examples

$\frac{3 x + 5}{2 (\frac{x + 1}{4 x}) - 1}$

Step 1

Simplify the denominator.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Factor $2$ out of $4 x$ .

$\frac{3 x + 5}{2 \frac{x + 1}{2 (2 x)} - 1}$

Step 1.1.2

Cancel the common factor.

$\frac{3 x + 5}{2 \frac{x + 1}{2 (2 x)} - 1}$

Step 1.1.3

Rewrite the expression.

$\frac{3 x + 5}{\frac{x + 1}{2 x} - 1}$

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{3 x + 5}{\frac{x + 1}{2 x} - 1 \cdot \frac{2 x}{2 x}}$

Step 1.3

Combine $- 1$ and $\frac{2 x}{2 x}$ .

$\frac{3 x + 5}{\frac{x + 1}{2 x} + \frac{- (2 x)}{2 x}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 x + 5}{\frac{x + 1 - (2 x)}{2 x}}$

Step 1.5

Reorder terms.

$\frac{3 x + 5}{\frac{- 1 \cdot 2 x + x + 1}{2 x}}$

Step 1.6

Rewrite $\frac{- 1 \cdot 2 x + x + 1}{2 x}$ in a factored form.

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Step 1.6.1

Multiply $- 1$ by $2$ .

$\frac{3 x + 5}{\frac{- 2 x + x + 1}{2 x}}$

Step 1.6.2

Add $- 2 x$ and $x$ .

$\frac{3 x + 5}{\frac{- x + 1}{2 x}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(3 x + 5) \frac{2 x}{- x + 1}$

Step 3

Multiply $3 x + 5$ by $\frac{2 x}{- x + 1}$ .

$\frac{(3 x + 5) (2 x)}{- x + 1}$

Step 4

Move $2$ to the left of $3 x + 5$ .

$\frac{2 \cdot (3 x + 5) x}{- x + 1}$

Step 5

Factor $- 1$ out of $- x$ .

$\frac{2 (3 x + 5) x}{- (x) + 1}$

Step 6

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{2 (3 x + 5) x}{- (x) - 1 (- 1)}$

Step 7

Factor $- 1$ out of $- (x) - 1 (- 1)$ .

$\frac{2 (3 x + 5) x}{- (x - 1)}$

Step 8

Rewrite negatives.

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Step 8.1

Rewrite $- (x - 1)$ as $- 1 (x - 1)$ .

$\frac{2 (3 x + 5) x}{- 1 (x - 1)}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{2 (3 x + 5) x}{x - 1}$

Step 8.3

Reorder factors in $- \frac{2 (3 x + 5) x}{x - 1}$ .

$- \frac{2 x (3 x + 5)}{x - 1}$