Solve 10x/5x+4-1/x+9=2

$$\frac { 10 x } { 5 x + 4 } - \frac { 1 } { x + 9 } = 2$$

Solve for x

$$x = -\frac{76}{13} = -5\frac{11}{13} \approx -5.846153846$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -9,-\frac{4}{5} since division by zero is not defined. Multiply both sides of the equation by \left(x+9\right)\left(5x+4\right), the least common multiple of 5x+4,x+9.

$$\left(x+9\right)\times 10x-\left(5x+4\right)=2\left(x+9\right)\left(5x+4\right)$$

Use the distributive property to multiply x+9 by 10.

$$\left(10x+90\right)x-\left(5x+4\right)=2\left(x+9\right)\left(5x+4\right)$$

Use the distributive property to multiply 10x+90 by x.

$$10x^{2}+90x-\left(5x+4\right)=2\left(x+9\right)\left(5x+4\right)$$

To find the opposite of 5x+4, find the opposite of each term.

$$10x^{2}+90x-5x-4=2\left(x+9\right)\left(5x+4\right)$$

Combine 90x and -5x to get 85x.

$$10x^{2}+85x-4=2\left(x+9\right)\left(5x+4\right)$$

Use the distributive property to multiply 2 by x+9.

$$10x^{2}+85x-4=\left(2x+18\right)\left(5x+4\right)$$

Use the distributive property to multiply 2x+18 by 5x+4 and combine like terms.

$$10x^{2}+85x-4=10x^{2}+98x+72$$

Subtract 10x^{2} from both sides.

$$10x^{2}+85x-4-10x^{2}=98x+72$$

Combine 10x^{2} and -10x^{2} to get 0.

$$85x-4=98x+72$$

Subtract 98x from both sides.

$$85x-4-98x=72$$

Combine 85x and -98x to get -13x.

$$-13x-4=72$$

Add 4 to both sides.

$$-13x=72+4$$

Add 72 and 4 to get 76.

$$-13x=76$$

Divide both sides by -13.

$$x=\frac{76}{-13}$$

Fraction \frac{76}{-13} can be rewritten as -\frac{76}{13} by extracting the negative sign.

$$x=-\frac{76}{13}$$