Solve 2b/b+3=3/b-10+2

$$\frac { 2 b } { b + 3 } = \frac { 3 } { b - 10 } + 2$$

Solve for b

$$b = \frac{17}{3} = 5\frac{2}{3} \approx 5.666666667$$

Steps for Solving Linear Equation

Variable b cannot be equal to any of the values -3,10 since division by zero is not defined. Multiply both sides of the equation by \left(b-10\right)\left(b+3\right), the least common multiple of b+3,b-10.

$$\left(b-10\right)\times 2b=\left(b+3\right)\times 3+\left(b-10\right)\left(b+3\right)\times 2$$

Use the distributive property to multiply b-10 by 2.

$$\left(2b-20\right)b=\left(b+3\right)\times 3+\left(b-10\right)\left(b+3\right)\times 2$$

Use the distributive property to multiply 2b-20 by b.

$$2b^{2}-20b=\left(b+3\right)\times 3+\left(b-10\right)\left(b+3\right)\times 2$$

Use the distributive property to multiply b+3 by 3.

$$2b^{2}-20b=3b+9+\left(b-10\right)\left(b+3\right)\times 2$$

Use the distributive property to multiply b-10 by b+3 and combine like terms.

$$2b^{2}-20b=3b+9+\left(b^{2}-7b-30\right)\times 2$$

Use the distributive property to multiply b^{2}-7b-30 by 2.

$$2b^{2}-20b=3b+9+2b^{2}-14b-60$$

Combine 3b and -14b to get -11b.

$$2b^{2}-20b=-11b+9+2b^{2}-60$$

Subtract 60 from 9 to get -51.

$$2b^{2}-20b=-11b-51+2b^{2}$$

Add 11b to both sides.

$$2b^{2}-20b+11b=-51+2b^{2}$$

Combine -20b and 11b to get -9b.

$$2b^{2}-9b=-51+2b^{2}$$

Subtract 2b^{2} from both sides.

$$2b^{2}-9b-2b^{2}=-51$$

Combine 2b^{2} and -2b^{2} to get 0.

$$-9b=-51$$

Divide both sides by -9.

$$b=\frac{-51}{-9}$$

Reduce the fraction \frac{-51}{-9} to lowest terms by extracting and canceling out -3.

$$b=\frac{17}{3}$$