<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] An alternate way is to break the problem down into simple workable parts:
$$\frac{x^5y^2x^3+x^4y^5−y^5x^7y^4}{x^4y^3}$$
$$=\frac{x^5y^2x^3}{x^4y^3}+\frac{x^4y^5}{x^4y^3}-\frac{y^5x^7y^4}{x^4y^3}$$
$$=\frac{x^8y^2}{x^4y^3}+\frac{x^4y^5}{x^4y^3}-\frac{x^7y^9}{x^4y^3}$$
$$=\frac{x^4}{y}+y^2-x^3y^6,\quad x\not=0.$$
This is equivalent to the answers given above.
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