Examples

\frac{5}{x + 1} + \frac{9}{x + 4}

$\frac{5}{x + 1} + \frac{9}{x + 4}$

Step 1

To write

\frac{5}{x + 1}

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

\frac{x + 4}{x + 4}

$\frac{x + 4}{x + 4}$ .

\frac{5}{x + 1} \cdot \frac{x + 4}{x + 4} + \frac{9}{x + 4}

$\frac{5}{x + 1} \cdot \frac{x + 4}{x + 4} + \frac{9}{x + 4}$

Step 2

To write

\frac{9}{x + 4}

$\frac{9}{x + 4}$ as a fraction with a common denominator, multiply by

\frac{x + 1}{x + 1}

$\frac{x + 1}{x + 1}$ .

\frac{5}{x + 1} \cdot \frac{x + 4}{x + 4} + \frac{9}{x + 4} \cdot \frac{x + 1}{x + 1}

$\frac{5}{x + 1} \cdot \frac{x + 4}{x + 4} + \frac{9}{x + 4} \cdot \frac{x + 1}{x + 1}$

Step 3

Write each expression with a common denominator of

(x + 1) (x + 4)

$(x + 1) (x + 4)$ , by multiplying each by an appropriate factor of

1

$1$ .

Tap for more steps...

Step 3.1

Multiply

\frac{5}{x + 1}

$\frac{5}{x + 1}$ by

\frac{x + 4}{x + 4}

$\frac{x + 4}{x + 4}$ .

\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9}{x + 4} \cdot \frac{x + 1}{x + 1}

$\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9}{x + 4} \cdot \frac{x + 1}{x + 1}$

Step 3.2

Multiply

\frac{9}{x + 4}

$\frac{9}{x + 4}$ by

\frac{x + 1}{x + 1}

$\frac{x + 1}{x + 1}$ .

\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9 (x + 1)}{(x + 4) (x + 1)}

$\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9 (x + 1)}{(x + 4) (x + 1)}$

Step 3.3

Reorder the factors of

(x + 4) (x + 1)

$(x + 4) (x + 1)$ .

\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9 (x + 1)}{(x + 1) (x + 4)}

$\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9 (x + 1)}{(x + 1) (x + 4)}$

\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9 (x + 1)}{(x + 1) (x + 4)}

$\frac{5 (x + 4)}{(x + 1) (x + 4)} + \frac{9 (x + 1)}{(x + 1) (x + 4)}$

Step 4

Combine the numerators over the common denominator.

\frac{5 (x + 4) + 9 (x + 1)}{(x + 1) (x + 4)}

$\frac{5 (x + 4) + 9 (x + 1)}{(x + 1) (x + 4)}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

\frac{5 x + 5 \cdot 4 + 9 (x + 1)}{(x + 1) (x + 4)}

$\frac{5 x + 5 \cdot 4 + 9 (x + 1)}{(x + 1) (x + 4)}$

Step 5.2

Multiply

5

$5$ by

4

$4$ .

\frac{5 x + 20 + 9 (x + 1)}{(x + 1) (x + 4)}

$\frac{5 x + 20 + 9 (x + 1)}{(x + 1) (x + 4)}$

Step 5.3

Apply the distributive property.

\frac{5 x + 20 + 9 x + 9 \cdot 1}{(x + 1) (x + 4)}

$\frac{5 x + 20 + 9 x + 9 \cdot 1}{(x + 1) (x + 4)}$

Step 5.4

Multiply

9

$9$ by

1

$1$ .

\frac{5 x + 20 + 9 x + 9}{(x + 1) (x + 4)}

$\frac{5 x + 20 + 9 x + 9}{(x + 1) (x + 4)}$

Step 5.5

Add

5 x

$5 x$ and

9 x

$9 x$ .

\frac{14 x + 20 + 9}{(x + 1) (x + 4)}

$\frac{14 x + 20 + 9}{(x + 1) (x + 4)}$

Step 5.6

Add

20

$20$ and

9

$9$ .

\frac{14 x + 29}{(x + 1) (x + 4)}

$\frac{14 x + 29}{(x + 1) (x + 4)}$

\frac{14 x + 29}{(x + 1) (x + 4)}

$\frac{14 x + 29}{(x + 1) (x + 4)}$

Enter YOUR Problem