Question

How do you simplify this?x²y+xy² / y²+2/5 × xy​​​

Answer 1

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

• How do you simplify this?
• x²y+xy² / y²+2/5 × xy

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$\sf\frac{ { x }^{ 2 } y+x { y }^{ 2 } }{ { y }^{ 2 } + \frac{ 2 }{ 5 } \times xy }$

Factor the expressions that are not already factored.

_____

How to factorise :-

NUMERATOR $\downarrow$

$\sf \: x ^ { 2 } y + x y ^ { 2 }$

Factor out xy.

$\sf \: xy\left(x+y\right)$

DENOMINATOR $\downarrow$

$\sf{ y }^{ 2 } + \frac{ 2 }{ 5 } \times xy$

Factor out 1/5.

$\sf \: {\frac{1}{5}y\left(2x+5y\right)}$

_____

Continuing...

$\sf\frac{xy\left(x+y\right)}{\frac{1}{5}y\left(2x+5y\right)}$

Cancel out y in both the numerator and denominator.

$\sf\frac{x\left(x+y\right)}{\frac{1}{5}\left(2x+5y\right)}$

Expand the expression.

$\sf\frac{x^{2}+xy}{\frac{2}{5}x+y}$

This can further simplified to as $\downarrow$

$= \boxed{\boxed{\bf\frac{5x\left(x +y\right)}{2x+5y}}}$