Solve 7/a+7=12/r-12

$$\frac { 7 } { a + 7 } = \frac { 12 } { r - 12 }$$

Solve for a

$$a=\frac{7\left(r-24\right)}{12}$$

$$r\neq 12$$

Steps for Solving Linear Equation

Variable a cannot be equal to -7 since division by zero is not defined. Multiply both sides of the equation by \left(r-12\right)\left(a+7\right), the least common multiple of a+7,r-12.

$$\left(r-12\right)\times 7=\left(a+7\right)\times 12$$

Use the distributive property to multiply r-12 by 7.

$$7r-84=\left(a+7\right)\times 12$$

Use the distributive property to multiply a+7 by 12.

$$7r-84=12a+84$$

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

$$12a+84=7r-84$$

Subtract 84 from both sides.

$$12a=7r-84-84$$

Subtract 84 from -84 to get -168.

$$12a=7r-168$$

Divide both sides by 12.

$$\frac{12a}{12}=\frac{7r-168}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$a=\frac{7r-168}{12}$$

Divide -168+7r by 12.

$$a=\frac{7r}{12}-14$$

Variable a cannot be equal to -7.

$$a=\frac{7r}{12}-14\text{, }a\neq -7$$

Solve for r

$$r=\frac{12\left(a+14\right)}{7}$$

$$a\neq -7$$

Steps for Solving Linear Equation

Variable r cannot be equal to 12 since division by zero is not defined. Multiply both sides of the equation by \left(r-12\right)\left(a+7\right), the least common multiple of a+7,r-12.

$$\left(r-12\right)\times 7=\left(a+7\right)\times 12$$

Use the distributive property to multiply r-12 by 7.

$$7r-84=\left(a+7\right)\times 12$$

Use the distributive property to multiply a+7 by 12.

$$7r-84=12a+84$$

Add 84 to both sides.

$$7r=12a+84+84$$

Add 84 and 84 to get 168.

$$7r=12a+168$$

Divide both sides by 7.

$$\frac{7r}{7}=\frac{12a+168}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$r=\frac{12a+168}{7}$$

Divide 168+12a by 7.

$$r=\frac{12a}{7}+24$$

Variable r cannot be equal to 12.

$$r=\frac{12a}{7}+24\text{, }r\neq 12$$