Solve 1/2b^2-6a/b=9/4b^2

$$\frac { 1 } { 2 b ^ { 2 } } - \frac { 6 a } { b } = \frac { 9 } { 4 b ^ { 2 } }$$

Solve for a

$$a=-\frac{7}{24b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4b^{2}, the least common multiple of 2b^{2},b,4b^{2}.

$$2-4b\times 6a=9$$

Multiply 4 and 6 to get 24.

$$2-24ba=9$$

Subtract 2 from both sides.

$$-24ba=9-2$$

Subtract 2 from 9 to get 7.

$$-24ba=7$$

Divide both sides by -1.

$$24ba=-7$$

Divide both sides by 24b.

$$\frac{24ba}{24b}=-\frac{7}{24b}$$

Dividing by 24b undoes the multiplication by 24b.

$$a=-\frac{7}{24b}$$

Solve for b

$$b=-\frac{7}{24a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4b^{2}, the least common multiple of 2b^{2},b,4b^{2}.

$$2-4b\times 6a=9$$

Multiply 4 and 6 to get 24.

$$2-24ba=9$$

Subtract 2 from both sides.

$$-24ba=9-2$$

Subtract 2 from 9 to get 7.

$$-24ba=7$$

Divide both sides by -1.

$$24ba=-7$$

The equation is in standard form.

$$24ab=-7$$

Divide both sides by 24a.

$$\frac{24ab}{24a}=-\frac{7}{24a}$$

Dividing by 24a undoes the multiplication by 24a.

$$b=-\frac{7}{24a}$$

Variable b cannot be equal to 0.

$$b=-\frac{7}{24a}\text{, }b\neq 0$$