Solve x^ 2 -5^ 2 x^ 3 +9^ 3 * (x-y)^ 2 +xy x^ 2 -xy / (x+1)^ 2 -2^ x ) x^ 3 +xy^ 2 | 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

$$\frac{x^{2}-5^{2}}{x^{3}+9^{3}}\times\frac{(x-y)^{2}+xy}{x^{2}-xy}\div\frac{(x+1)^{2}-2^{x})}{x^{3}+xy^{2}}$$

Evaluate

$\frac{x^{2}+y^{2}}{x^{2}+2xy+4y^{2}}$

Short Solution Steps

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

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

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

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

Multiply $\frac{x-y}{x^{2}-xy+y^{2}}$ times $\frac{\left(x-y\right)^{2}+xy}{x^{2}-xy}$ by multiplying numerator times numerator and denominator times denominator.

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

Divide $\frac{\left(x-y\right)\left(\left(x-y\right)^{2}+xy\right)}{\left(x^{2}-xy+y^{2}\right)\left(x^{2}-xy\right)}$ by $\frac{\left(x+2y\right)^{2}-2xy}{x^{3}+xy^{2}}$ by multiplying $\frac{\left(x-y\right)\left(\left(x-y\right)^{2}+xy\right)}{\left(x^{2}-xy+y^{2}\right)\left(x^{2}-xy\right)}$ by the reciprocal of $\frac{\left(x+2y\right)^{2}-2xy}{x^{3}+xy^{2}}$.

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

Factor the expressions that are not already factored.

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

Cancel out $x\left(x-y\right)\left(x^{2}-xy+y^{2}\right)$ in both numerator and denominator.

$$\frac{x^{2}+y^{2}}{x^{2}+2xy+4y^{2}}$$

Expand

$\frac{x^{2}+y^{2}}{x^{2}+2xy+4y^{2}}$

Short Solution Steps

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

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

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

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

Multiply $\frac{x-y}{x^{2}-xy+y^{2}}$ times $\frac{\left(x-y\right)^{2}+xy}{x^{2}-xy}$ by multiplying numerator times numerator and denominator times denominator.

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

Divide $\frac{\left(x-y\right)\left(\left(x-y\right)^{2}+xy\right)}{\left(x^{2}-xy+y^{2}\right)\left(x^{2}-xy\right)}$ by $\frac{\left(x+2y\right)^{2}-2xy}{x^{3}+xy^{2}}$ by multiplying $\frac{\left(x-y\right)\left(\left(x-y\right)^{2}+xy\right)}{\left(x^{2}-xy+y^{2}\right)\left(x^{2}-xy\right)}$ by the reciprocal of $\frac{\left(x+2y\right)^{2}-2xy}{x^{3}+xy^{2}}$.

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

Factor the expressions that are not already factored.

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

Cancel out $x\left(x-y\right)\left(x^{2}-xy+y^{2}\right)$ in both numerator and denominator.

$$\frac{x^{2}+y^{2}}{x^{2}+2xy+4y^{2}}$$