Solve 70x/10x+5+61/x+13=7

$$\frac { 70 x } { 10 x + 5 } + \frac { 61 } { x + 13 } = 7$$

Solve for x

$$x=\frac{6}{23}\approx 0.260869565$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -13,-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 5\left(x+13\right)\left(2x+1\right), the least common multiple of 10x+5,x+13.

$$\left(x+13\right)\times 70x+\left(10x+5\right)\times 61=35\left(x+13\right)\left(2x+1\right)$$

Use the distributive property to multiply x+13 by 70.

$$\left(70x+910\right)x+\left(10x+5\right)\times 61=35\left(x+13\right)\left(2x+1\right)$$

Use the distributive property to multiply 70x+910 by x.

$$70x^{2}+910x+\left(10x+5\right)\times 61=35\left(x+13\right)\left(2x+1\right)$$

Use the distributive property to multiply 10x+5 by 61.

$$70x^{2}+910x+610x+305=35\left(x+13\right)\left(2x+1\right)$$

Combine 910x and 610x to get 1520x.

$$70x^{2}+1520x+305=35\left(x+13\right)\left(2x+1\right)$$

Use the distributive property to multiply 35 by x+13.

$$70x^{2}+1520x+305=\left(35x+455\right)\left(2x+1\right)$$

Use the distributive property to multiply 35x+455 by 2x+1 and combine like terms.

$$70x^{2}+1520x+305=70x^{2}+945x+455$$

Subtract 70x^{2} from both sides.

$$70x^{2}+1520x+305-70x^{2}=945x+455$$

Combine 70x^{2} and -70x^{2} to get 0.

$$1520x+305=945x+455$$

Subtract 945x from both sides.

$$1520x+305-945x=455$$

Combine 1520x and -945x to get 575x.

$$575x+305=455$$

Subtract 305 from both sides.

$$575x=455-305$$

Subtract 305 from 455 to get 150.

$$575x=150$$

Divide both sides by 575.

$$x=\frac{150}{575}$$

Reduce the fraction \frac{150}{575} to lowest terms by extracting and canceling out 25.

$$x=\frac{6}{23}$$