Solve 9/b+9=8/r-8

$$\frac { 9 } { b + 9 } = \frac { 8 } { r - 8 }$$

Solve for b

$$b=\frac{9\left(r-16\right)}{8}$$

$$r\neq 8$$

Steps for Solving Linear Equation

Variable b cannot be equal to -9 since division by zero is not defined. Multiply both sides of the equation by \left(r-8\right)\left(b+9\right), the least common multiple of b+9,r-8.

$$\left(r-8\right)\times 9=\left(b+9\right)\times 8$$

Use the distributive property to multiply r-8 by 9.

$$9r-72=\left(b+9\right)\times 8$$

Use the distributive property to multiply b+9 by 8.

$$9r-72=8b+72$$

Swap sides so that all variable terms are on the left hand side.

$$8b+72=9r-72$$

Subtract 72 from both sides.

$$8b=9r-72-72$$

Subtract 72 from -72 to get -144.

$$8b=9r-144$$

Divide both sides by 8.

$$\frac{8b}{8}=\frac{9r-144}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$b=\frac{9r-144}{8}$$

Divide -144+9r by 8.

$$b=\frac{9r}{8}-18$$

Variable b cannot be equal to -9.

$$b=\frac{9r}{8}-18\text{, }b\neq -9$$

Solve for r

$$r=\frac{8\left(b+18\right)}{9}$$

$$b\neq -9$$

Steps for Solving Linear Equation

Variable r cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by \left(r-8\right)\left(b+9\right), the least common multiple of b+9,r-8.

$$\left(r-8\right)\times 9=\left(b+9\right)\times 8$$

Use the distributive property to multiply r-8 by 9.

$$9r-72=\left(b+9\right)\times 8$$

Use the distributive property to multiply b+9 by 8.

$$9r-72=8b+72$$

Add 72 to both sides.

$$9r=8b+72+72$$

Add 72 and 72 to get 144.

$$9r=8b+144$$

Divide both sides by 9.

$$\frac{9r}{9}=\frac{8b+144}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$r=\frac{8b+144}{9}$$

Divide 144+8b by 9.

$$r=\frac{8b}{9}+16$$

Variable r cannot be equal to 8.

$$r=\frac{8b}{9}+16\text{, }r\neq 8$$