Solve 90x/15x+6+51/x+15=6

$$\frac { 90 x } { 15 x + 6 } + \frac { 51 } { x + 15 } = 6$$

Solve for x

$$x=\frac{26}{81}\approx 0.320987654$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -15,-\frac{2}{5} since division by zero is not defined. Multiply both sides of the equation by 3\left(x+15\right)\left(5x+2\right), the least common multiple of 15x+6,x+15.

$$\left(x+15\right)\times 90x+\left(15x+6\right)\times 51=18\left(x+15\right)\left(5x+2\right)$$

Use the distributive property to multiply x+15 by 90.

$$\left(90x+1350\right)x+\left(15x+6\right)\times 51=18\left(x+15\right)\left(5x+2\right)$$

Use the distributive property to multiply 90x+1350 by x.

$$90x^{2}+1350x+\left(15x+6\right)\times 51=18\left(x+15\right)\left(5x+2\right)$$

Use the distributive property to multiply 15x+6 by 51.

$$90x^{2}+1350x+765x+306=18\left(x+15\right)\left(5x+2\right)$$

Combine 1350x and 765x to get 2115x.

$$90x^{2}+2115x+306=18\left(x+15\right)\left(5x+2\right)$$

Use the distributive property to multiply 18 by x+15.

$$90x^{2}+2115x+306=\left(18x+270\right)\left(5x+2\right)$$

Use the distributive property to multiply 18x+270 by 5x+2 and combine like terms.

$$90x^{2}+2115x+306=90x^{2}+1386x+540$$

Subtract 90x^{2} from both sides.

$$90x^{2}+2115x+306-90x^{2}=1386x+540$$

Combine 90x^{2} and -90x^{2} to get 0.

$$2115x+306=1386x+540$$

Subtract 1386x from both sides.

$$2115x+306-1386x=540$$

Combine 2115x and -1386x to get 729x.

$$729x+306=540$$

Subtract 306 from both sides.

$$729x=540-306$$

Subtract 306 from 540 to get 234.

$$729x=234$$

Divide both sides by 729.

$$x=\frac{234}{729}$$

Reduce the fraction \frac{234}{729} to lowest terms by extracting and canceling out 9.

$$x=\frac{26}{81}$$