Solve 5/2+a=1/b-6

$$\frac { 5 } { 2 + a } = \frac { 1 } { b - 6 }$$

Solve for a

$$a=5b-32$$

$$b\neq 6$$

Solution Steps

Variable a cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by \left(b-6\right)\left(a+2\right), the least common multiple of 2+a,b-6.

$$\left(b-6\right)\times 5=a+2$$

Use the distributive property to multiply b-6 by 5.

$$5b-30=a+2$$

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

$$a+2=5b-30$$

Subtract 2 from both sides.

$$a=5b-30-2$$

Subtract 2 from -30 to get -32.

$$a=5b-32$$

Variable a cannot be equal to -2.

$$a=5b-32\text{, }a\neq -2$$

Solve for b

$$b=\frac{a+32}{5}$$

$$a\neq -2$$

Steps for Solving Linear Equation

Variable b cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by \left(b-6\right)\left(a+2\right), the least common multiple of 2+a,b-6.

$$\left(b-6\right)\times 5=a+2$$

Use the distributive property to multiply b-6 by 5.

$$5b-30=a+2$$

Add 30 to both sides.

$$5b=a+2+30$$

Add 2 and 30 to get 32.

$$5b=a+32$$

Divide both sides by 5.

$$\frac{5b}{5}=\frac{a+32}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$b=\frac{a+32}{5}$$

Variable b cannot be equal to 6.

$$b=\frac{a+32}{5}\text{, }b\neq 6$$