Solve by Factoring (2x-1)/(x+2)=4/5

$\frac{2 x - 1}{x + 2} = \frac{4}{5}$

Step 1

Subtract $\frac{4}{5}$ from both sides of the equation.

$\frac{2 x - 1}{x + 2} - \frac{4}{5} = 0$

Step 2

Simplify $\frac{2 x - 1}{x + 2} - \frac{4}{5}$ .

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

$\frac{2 x - 1}{x + 2} \cdot \frac{5}{5} - \frac{4}{5} = 0$

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$\frac{2 x - 1}{x + 2} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{x + 2}{x + 2} = 0$

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

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

$\frac{(2 x - 1) \cdot 5}{(x + 2) \cdot 5} - \frac{4}{5} \cdot \frac{x + 2}{x + 2} = 0$

Multiply $\frac{4}{5}$ by $\frac{x + 2}{x + 2}$ .

$\frac{(2 x - 1) \cdot 5}{(x + 2) \cdot 5} - \frac{4 (x + 2)}{5 (x + 2)} = 0$

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

$\frac{(2 x - 1) \cdot 5}{5 (x + 2)} - \frac{4 (x + 2)}{5 (x + 2)} = 0$

Combine the numerators over the common denominator.

$\frac{(2 x - 1) \cdot 5 - 4 (x + 2)}{5 (x + 2)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{2 x \cdot 5 - 1 \cdot 5 - 4 (x + 2)}{5 (x + 2)} = 0$

Multiply $5$ by $2$ .

$\frac{10 x - 1 \cdot 5 - 4 (x + 2)}{5 (x + 2)} = 0$

Multiply $- 1$ by $5$ .

$\frac{10 x - 5 - 4 (x + 2)}{5 (x + 2)} = 0$

Apply the distributive property.

$\frac{10 x - 5 - 4 x - 4 \cdot 2}{5 (x + 2)} = 0$

Multiply $- 4$ by $2$ .

$\frac{10 x - 5 - 4 x - 8}{5 (x + 2)} = 0$

Subtract $4 x$ from $10 x$ .

$\frac{6 x - 5 - 8}{5 (x + 2)} = 0$

Subtract $8$ from $- 5$ .

$\frac{6 x - 13}{5 (x + 2)} = 0$

Step 3

Set the numerator equal to zero.

$6 x - 13 = 0$

Step 4

Solve the equation for $x$ .

Add $13$ to both sides of the equation.

$6 x = 13$

Divide each term in $6 x = 13$ by $6$ and simplify.

Divide each term in $6 x = 13$ by $6$ .

$\frac{6 x}{6} = \frac{13}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{13}{6}$

Divide $x$ by $1$ .

$x = \frac{13}{6}$

Solve by Factoring (2x-1)/(x+2)=4/5

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