Solve by Factoring 10/(6x+7)=6/(2x+9)

$\frac{10}{6 x + 7} = \frac{6}{2 x + 9}$

Step 1

Subtract $\frac{6}{2 x + 9}$ from both sides of the equation.

$\frac{10}{6 x + 7} - \frac{6}{2 x + 9} = 0$

Step 2

Simplify $\frac{10}{6 x + 7} - \frac{6}{2 x + 9}$ .

To write $\frac{10}{6 x + 7}$ as a fraction with a common denominator, multiply by $\frac{2 x + 9}{2 x + 9}$ .

$\frac{10}{6 x + 7} \cdot \frac{2 x + 9}{2 x + 9} - \frac{6}{2 x + 9} = 0$

To write $- \frac{6}{2 x + 9}$ as a fraction with a common denominator, multiply by $\frac{6 x + 7}{6 x + 7}$ .

$\frac{10}{6 x + 7} \cdot \frac{2 x + 9}{2 x + 9} - \frac{6}{2 x + 9} \cdot \frac{6 x + 7}{6 x + 7} = 0$

Write each expression with a common denominator of $(6 x + 7) (2 x + 9)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{10}{6 x + 7}$ by $\frac{2 x + 9}{2 x + 9}$ .

$\frac{10 (2 x + 9)}{(6 x + 7) (2 x + 9)} - \frac{6}{2 x + 9} \cdot \frac{6 x + 7}{6 x + 7} = 0$

Multiply $\frac{6}{2 x + 9}$ by $\frac{6 x + 7}{6 x + 7}$ .

$\frac{10 (2 x + 9)}{(6 x + 7) (2 x + 9)} - \frac{6 (6 x + 7)}{(2 x + 9) (6 x + 7)} = 0$

Reorder the factors of $(6 x + 7) (2 x + 9)$ .

$\frac{10 (2 x + 9)}{(2 x + 9) (6 x + 7)} - \frac{6 (6 x + 7)}{(2 x + 9) (6 x + 7)} = 0$

Combine the numerators over the common denominator.

$\frac{10 (2 x + 9) - 6 (6 x + 7)}{(2 x + 9) (6 x + 7)} = 0$

Simplify the numerator.

Factor $2$ out of $10 (2 x + 9) - 6 (6 x + 7)$ .

Factor $2$ out of $10 (2 x + 9)$ .

$\frac{2 (5 (2 x + 9)) - 6 (6 x + 7)}{(2 x + 9) (6 x + 7)} = 0$

Factor $2$ out of $- 6 (6 x + 7)$ .

$\frac{2 (5 (2 x + 9)) + 2 (- 3 (6 x + 7))}{(2 x + 9) (6 x + 7)} = 0$

Factor $2$ out of $2 (5 (2 x + 9)) + 2 (- 3 (6 x + 7))$ .

$\frac{2 (5 (2 x + 9) - 3 (6 x + 7))}{(2 x + 9) (6 x + 7)} = 0$

Apply the distributive property.

$\frac{2 (5 (2 x) + 5 \cdot 9 - 3 (6 x + 7))}{(2 x + 9) (6 x + 7)} = 0$

Multiply $2$ by $5$ .

$\frac{2 (10 x + 5 \cdot 9 - 3 (6 x + 7))}{(2 x + 9) (6 x + 7)} = 0$

Multiply $5$ by $9$ .

$\frac{2 (10 x + 45 - 3 (6 x + 7))}{(2 x + 9) (6 x + 7)} = 0$

Apply the distributive property.

$\frac{2 (10 x + 45 - 3 (6 x) - 3 \cdot 7)}{(2 x + 9) (6 x + 7)} = 0$

Multiply $6$ by $- 3$ .

$\frac{2 (10 x + 45 - 18 x - 3 \cdot 7)}{(2 x + 9) (6 x + 7)} = 0$

Multiply $- 3$ by $7$ .

$\frac{2 (10 x + 45 - 18 x - 21)}{(2 x + 9) (6 x + 7)} = 0$

Subtract $18 x$ from $10 x$ .

$\frac{2 (- 8 x + 45 - 21)}{(2 x + 9) (6 x + 7)} = 0$

Subtract $21$ from $45$ .

$\frac{2 (- 8 x + 24)}{(2 x + 9) (6 x + 7)} = 0$

Factor $8$ out of $- 8 x + 24$ .

Factor $8$ out of $- 8 x$ .

$\frac{2 (8 (- x) + 24)}{(2 x + 9) (6 x + 7)} = 0$

Factor $8$ out of $24$ .

$\frac{2 (8 (- x) + 8 (3))}{(2 x + 9) (6 x + 7)} = 0$

Factor $8$ out of $8 (- x) + 8 (3)$ .

$\frac{2 (8 (- x + 3))}{(2 x + 9) (6 x + 7)} = 0$

$\frac{2 \cdot 8 (- x + 3)}{(2 x + 9) (6 x + 7)} = 0$

Multiply $2$ by $8$ .

$\frac{16 (- x + 3)}{(2 x + 9) (6 x + 7)} = 0$

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

$\frac{16 (- (x) + 3)}{(2 x + 9) (6 x + 7)} = 0$

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{16 (- (x) - 1 (- 3))}{(2 x + 9) (6 x + 7)} = 0$

Factor $- 1$ out of $- (x) - 1 (- 3)$ .

$\frac{16 (- (x - 3))}{(2 x + 9) (6 x + 7)} = 0$

Rewrite $- (x - 3)$ as $- 1 (x - 3)$ .

$\frac{16 (- 1 (x - 3))}{(2 x + 9) (6 x + 7)} = 0$

Move the negative in front of the fraction.

$- \frac{16 (x - 3)}{(2 x + 9) (6 x + 7)} = 0$

Step 3

Set the numerator equal to zero.

$16 (x - 3) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $16 (x - 3) = 0$ by $16$ and simplify.

Divide each term in $16 (x - 3) = 0$ by $16$ .

$\frac{16 (x - 3)}{16} = \frac{0}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 (x - 3)}{16} = \frac{0}{16}$

Divide $x - 3$ by $1$ .

$x - 3 = \frac{0}{16}$

Simplify the right side.

Divide $0$ by $16$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Solve by Factoring 10/(6x+7)=6/(2x+9)

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