Solve 3b/2x+3-b-x/x-5=1

$$\frac{ 3b }{ 2x+3 } - \frac{ b-x }{ x-5 } = 1$$

Solve for b

$$b=-\frac{5\left(2x+3\right)}{x-18}$$

$$x\neq 18\text{ and }x\neq -\frac{3}{2}\text{ and }x\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-5\right)\left(2x+3\right), the least common multiple of 2x+3,x-5.

$$\left(x-5\right)\times 3b-\left(2x+3\right)\left(b-x\right)=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply x-5 by 3.

$$\left(3x-15\right)b-\left(2x+3\right)\left(b-x\right)=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply 3x-15 by b.

$$3xb-15b-\left(2x+3\right)\left(b-x\right)=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply 2x+3 by b-x.

$$3xb-15b-\left(2xb-2x^{2}+3b-3x\right)=\left(x-5\right)\left(2x+3\right)$$

To find the opposite of 2xb-2x^{2}+3b-3x, find the opposite of each term.

$$3xb-15b-2xb+2x^{2}-3b+3x=\left(x-5\right)\left(2x+3\right)$$

Combine 3xb and -2xb to get xb.

$$xb-15b+2x^{2}-3b+3x=\left(x-5\right)\left(2x+3\right)$$

Combine -15b and -3b to get -18b.

$$xb-18b+2x^{2}+3x=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply x-5 by 2x+3 and combine like terms.

$$xb-18b+2x^{2}+3x=2x^{2}-7x-15$$

Subtract 2x^{2} from both sides.

$$xb-18b+3x=2x^{2}-7x-15-2x^{2}$$

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

$$xb-18b+3x=-7x-15$$

Subtract 3x from both sides.

$$xb-18b=-7x-15-3x$$

Combine -7x and -3x to get -10x.

$$xb-18b=-10x-15$$

Combine all terms containing b.

$$\left(x-18\right)b=-10x-15$$

Divide both sides by x-18.

$$\frac{\left(x-18\right)b}{x-18}=\frac{-10x-15}{x-18}$$

Dividing by x-18 undoes the multiplication by x-18.

$$b=\frac{-10x-15}{x-18}$$

Divide -10x-15 by x-18.

$$b=-\frac{5\left(2x+3\right)}{x-18}$$

Solve for x

$$x=-\frac{3\left(5-6b\right)}{b+10}$$

$$b\neq 0\text{ and }b\neq -10\text{ and }b\neq 5$$

Steps for Solving Linear Equation

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

$$\left(x-5\right)\times 3b-\left(2x+3\right)\left(b-x\right)=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply x-5 by 3.

$$\left(3x-15\right)b-\left(2x+3\right)\left(b-x\right)=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply 3x-15 by b.

$$3xb-15b-\left(2x+3\right)\left(b-x\right)=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply 2x+3 by b-x.

$$3xb-15b-\left(2xb-2x^{2}+3b-3x\right)=\left(x-5\right)\left(2x+3\right)$$

To find the opposite of 2xb-2x^{2}+3b-3x, find the opposite of each term.

$$3xb-15b-2xb+2x^{2}-3b+3x=\left(x-5\right)\left(2x+3\right)$$

Combine 3xb and -2xb to get xb.

$$xb-15b+2x^{2}-3b+3x=\left(x-5\right)\left(2x+3\right)$$

Combine -15b and -3b to get -18b.

$$xb-18b+2x^{2}+3x=\left(x-5\right)\left(2x+3\right)$$

Use the distributive property to multiply x-5 by 2x+3 and combine like terms.

$$xb-18b+2x^{2}+3x=2x^{2}-7x-15$$

Subtract 2x^{2} from both sides.

$$xb-18b+2x^{2}+3x-2x^{2}=-7x-15$$

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

$$xb-18b+3x=-7x-15$$

Add 7x to both sides.

$$xb-18b+3x+7x=-15$$

Combine 3x and 7x to get 10x.

$$xb-18b+10x=-15$$

Add 18b to both sides.

$$xb+10x=-15+18b$$

Combine all terms containing x.

$$\left(b+10\right)x=-15+18b$$

The equation is in standard form.

$$\left(b+10\right)x=18b-15$$

Divide both sides by b+10.

$$\frac{\left(b+10\right)x}{b+10}=\frac{18b-15}{b+10}$$

Dividing by b+10 undoes the multiplication by b+10.

$$x=\frac{18b-15}{b+10}$$

Divide -15+18b by b+10.

$$x=\frac{3\left(6b-5\right)}{b+10}$$

Variable x cannot be equal to any of the values -\frac{3}{2},5.

$$x=\frac{3\left(6b-5\right)}{b+10}\text{, }x\neq -\frac{3}{2}\text{ and }x\neq 5$$