Solve (3x ^ 2)/(x + y) + (6xy + 3y ^ 2)/(x + y) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{3x^{2}}{x+y}+\frac{6xy+3y^{2}}{x+y}$$

Evaluate

$3\left(x+y\right)$

Short Solution Steps

Since $\frac{3x^{2}}{x+y}$ and $\frac{6xy+3y^{2}}{x+y}$ have the same denominator, add them by adding their numerators.

$$\frac{3x^{2}+6xy+3y^{2}}{x+y}$$

Factor the expressions that are not already factored in $\frac{3x^{2}+6xy+3y^{2}}{x+y}$.

$$\frac{3\left(x+y\right)^{2}}{x+y}$$

Cancel out $x+y$ in both numerator and denominator.

$$3\left(x+y\right)$$

Expand the expression.

$$3x+3y$$

Expand

$3x+3y$

Short Solution Steps

Since $\frac{3x^{2}}{x+y}$ and $\frac{6xy+3y^{2}}{x+y}$ have the same denominator, add them by adding their numerators.

$$\frac{3x^{2}+6xy+3y^{2}}{x+y}$$

Factor the expressions that are not already factored in $\frac{3x^{2}+6xy+3y^{2}}{x+y}$.

$$\frac{3\left(x+y\right)^{2}}{x+y}$$

Cancel out $x+y$ in both numerator and denominator.

$$3\left(x+y\right)$$

Expand the expression.

$$3x+3y$$