Algebra Examples

$\frac{15}{x - 5} + 7 = \frac{25}{x - 5}$

Step 1

Subtract $\frac{25}{x - 5}$ from both sides of the equation.

$\frac{15}{x - 5} + 7 - \frac{25}{x - 5} = 0$

Step 2

Simplify $\frac{15}{x - 5} + 7 - \frac{25}{x - 5}$ .

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$7 + \frac{15 - 25}{x - 5} = 0$

Step 2.2

Subtract $25$ from $15$ .

$7 + \frac{- 10}{x - 5} = 0$

Step 2.3

Move the negative in front of the fraction.

$7 - \frac{10}{x - 5} = 0$

Step 2.4

To write $7$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

$\frac{7 (x - 5)}{x - 5} - \frac{10}{x - 5} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{7 (x - 5) - 10}{x - 5} = 0$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Apply the distributive property.

$\frac{7 x + 7 \cdot - 5 - 10}{x - 5} = 0$

Step 2.6.2

Multiply $7$ by $- 5$ .

$\frac{7 x - 35 - 10}{x - 5} = 0$

Step 2.6.3

Subtract $10$ from $- 35$ .

$\frac{7 x - 45}{x - 5} = 0$

Step 3

Set the numerator equal to zero.

$7 x - 45 = 0$

Step 4

Solve the equation for $x$ .

Tap for more steps...

Step 4.1

Add $45$ to both sides of the equation.

$7 x = 45$

Step 4.2

Divide each term in $7 x = 45$ by $7$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $7 x = 45$ by $7$ .

$\frac{7 x}{7} = \frac{45}{7}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{45}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{45}{7}$