<s>[INST] Indices - factorising Simplify: $$\frac {x^5y^2x^3 + x^4y^5 - y^5x^7y^4}{x^4y^3}$$
I know this is probably low level stuff but I need to be able to do this specific type of question and I have no way of checking my work. If anyone could offer a step by step working I'd be appreciative
 [/INST] You have
\begin{align*}
\frac {x^5y^2x^3 + x^4y^5 - y^5x^7y^4}{x^4y^3}
&=\frac {x^8y^2 + x^4y^5 - x^7y^9}{x^4y^3} \\
&=\frac {x^4y^2\big(x^4 + y^3 - x^3y^7\big)}{x^4y^3} \\
&=\frac {x^4 + y^3 - x^3y^7}{y},\quad x\not=0.
\end{align*}
That's about as far as you can go.
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