Solve x-18-8y^2/4y^2+9-12y/4y^2+9*4y^2+3/2y

$$x- \frac{ 18-8 { y }^{ 2 } }{ 4 { y }^{ 2 } +9 } - \frac{ 12y }{ 4 { y }^{ 2 } +9 } \times \frac{ 4 { y }^{ 2 } +3 }{ 2y }$$

Evaluate

$$x-4$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{4y^{2}+9}{4y^{2}+9}.

$$\frac{x\left(4y^{2}+9\right)}{4y^{2}+9}-\frac{18-8y^{2}}{4y^{2}+9}-\frac{12y}{4y^{2}+9}\times \frac{4y^{2}+3}{2y}$$

Since \frac{x\left(4y^{2}+9\right)}{4y^{2}+9} and \frac{18-8y^{2}}{4y^{2}+9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(4y^{2}+9\right)-\left(18-8y^{2}\right)}{4y^{2}+9}-\frac{12y}{4y^{2}+9}\times \frac{4y^{2}+3}{2y}$$

Do the multiplications in x\left(4y^{2}+9\right)-\left(18-8y^{2}\right).

$$\frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9}-\frac{12y}{4y^{2}+9}\times \frac{4y^{2}+3}{2y}$$

Multiply \frac{12y}{4y^{2}+9} times \frac{4y^{2}+3}{2y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9}-\frac{12y\left(4y^{2}+3\right)}{\left(4y^{2}+9\right)\times 2y}$$

Cancel out 2y in both numerator and denominator.

$$\frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9}-\frac{6\left(4y^{2}+3\right)}{4y^{2}+9}$$

Since \frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9} and \frac{6\left(4y^{2}+3\right)}{4y^{2}+9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4xy^{2}+9x-18+8y^{2}-6\left(4y^{2}+3\right)}{4y^{2}+9}$$

Do the multiplications in 4xy^{2}+9x-18+8y^{2}-6\left(4y^{2}+3\right).

$$\frac{4xy^{2}+9x-18+8y^{2}-24y^{2}-18}{4y^{2}+9}$$

Combine like terms in 4xy^{2}+9x-18+8y^{2}-24y^{2}-18.

$$\frac{4xy^{2}+9x-36-16y^{2}}{4y^{2}+9}$$

Factor the expressions that are not already factored in \frac{4xy^{2}+9x-36-16y^{2}}{4y^{2}+9}.

$$\frac{\left(x-4\right)\left(4y^{2}+9\right)}{4y^{2}+9}$$

Cancel out 4y^{2}+9 in both numerator and denominator.

$$x-4$$

Expand

$$x-4$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{4y^{2}+9}{4y^{2}+9}.

$$\frac{x\left(4y^{2}+9\right)}{4y^{2}+9}-\frac{18-8y^{2}}{4y^{2}+9}-\frac{12y}{4y^{2}+9}\times \frac{4y^{2}+3}{2y}$$

Since \frac{x\left(4y^{2}+9\right)}{4y^{2}+9} and \frac{18-8y^{2}}{4y^{2}+9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(4y^{2}+9\right)-\left(18-8y^{2}\right)}{4y^{2}+9}-\frac{12y}{4y^{2}+9}\times \frac{4y^{2}+3}{2y}$$

Do the multiplications in x\left(4y^{2}+9\right)-\left(18-8y^{2}\right).

$$\frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9}-\frac{12y}{4y^{2}+9}\times \frac{4y^{2}+3}{2y}$$

Multiply \frac{12y}{4y^{2}+9} times \frac{4y^{2}+3}{2y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9}-\frac{12y\left(4y^{2}+3\right)}{\left(4y^{2}+9\right)\times 2y}$$

Cancel out 2y in both numerator and denominator.

$$\frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9}-\frac{6\left(4y^{2}+3\right)}{4y^{2}+9}$$

Since \frac{4xy^{2}+9x-18+8y^{2}}{4y^{2}+9} and \frac{6\left(4y^{2}+3\right)}{4y^{2}+9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4xy^{2}+9x-18+8y^{2}-6\left(4y^{2}+3\right)}{4y^{2}+9}$$

Do the multiplications in 4xy^{2}+9x-18+8y^{2}-6\left(4y^{2}+3\right).

$$\frac{4xy^{2}+9x-18+8y^{2}-24y^{2}-18}{4y^{2}+9}$$

Combine like terms in 4xy^{2}+9x-18+8y^{2}-24y^{2}-18.

$$\frac{4xy^{2}+9x-36-16y^{2}}{4y^{2}+9}$$

Factor the expressions that are not already factored in \frac{4xy^{2}+9x-36-16y^{2}}{4y^{2}+9}.

$$\frac{\left(x-4\right)\left(4y^{2}+9\right)}{4y^{2}+9}$$

Cancel out 4y^{2}+9 in both numerator and denominator.

$$x-4$$