[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- How do you simplify this ⇨ x²y+xy² / y²+2/5 × xy
[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]
[tex] \sf\frac{ { x }^{ 2 } y+x { y }^{ 2 } }{ { y }^{ 2 } + \frac{ 2 }{ 5 } \times xy } \\ [/tex]
Factor the expressions that are not already factored.
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How to factorise :-
NUMERATOR [tex]\downarrow[/tex]
[tex] \sf \: x ^ { 2 } y + x y ^ { 2 }[/tex]
Factor out xy.
[tex] \sf \: xy\left(x+y\right) [/tex]
DENOMINATOR [tex]\downarrow[/tex]
[tex] \sf{ y }^{ 2 } + \frac{ 2 }{ 5 } \times xy \\ [/tex]
Factor out 1/5.
[tex] \sf \: {\frac{1}{5}y\left(2x+5y\right)} \\ [/tex]
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Continuing...
[tex] \sf\frac{xy\left(x+y\right)}{\frac{1}{5}y\left(2x+5y\right)} \\ [/tex]
Cancel out y in both the numerator and denominator.
[tex] \sf\frac{x\left(x+y\right)}{\frac{1}{5}\left(2x+5y\right)} \\ [/tex]
Expand the expression.
[tex] \sf\frac{x^{2}+xy}{\frac{2}{5}x+y} \\ [/tex]
This can further simplified to as [tex]\downarrow[/tex]
[tex] = \boxed{\boxed{\bf\frac{5x\left(x +y\right)}{2x+5y}}}[/tex]
