Algebra Examples

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

Step 1

To write $\frac{2}{2 x + 5}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

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

Step 2

To write $- \frac{3}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{2 x + 5}{2 x + 5}$ .

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

Step 3

Write each expression with a common denominator of $(2 x + 5) (x + 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Reorder the factors of $(x + 1) (2 x + 5)$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $2$ by $1$ .

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

Step 5.3

Apply the distributive property.

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

Step 5.4

Multiply $2$ by $- 3$ .

$\frac{2 x + 2 - 6 x - 3 \cdot 5}{(2 x + 5) (x + 1)}$

Step 5.5

Multiply $- 3$ by $5$ .

$\frac{2 x + 2 - 6 x - 15}{(2 x + 5) (x + 1)}$

Step 5.6

Subtract $6 x$ from $2 x$ .

$\frac{- 4 x + 2 - 15}{(2 x + 5) (x + 1)}$

Step 5.7

Subtract $15$ from $2$ .

$\frac{- 4 x - 13}{(2 x + 5) (x + 1)}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) - 13}{(2 x + 5) (x + 1)}$

Step 6.2

Rewrite $- 13$ as $- 1 (13)$ .

$\frac{- (4 x) - 1 (13)}{(2 x + 5) (x + 1)}$

Step 6.3

Factor $- 1$ out of $- (4 x) - 1 (13)$ .

$\frac{- (4 x + 13)}{(2 x + 5) (x + 1)}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (4 x + 13)$ as $- 1 (4 x + 13)$ .

$\frac{- 1 (4 x + 13)}{(2 x + 5) (x + 1)}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{4 x + 13}{(2 x + 5) (x + 1)}$