How do you simplify #\frac { \frac { 1} { a x ^ { 8} y } - \frac { 1} { x y ^ { 6} } } { \frac { 1} { a b x ^ { 7} y ^ { 5} } + \frac { 1} { b x y } }#?

1 Answer
Somebody N.
Nov 11, 2017

# ((ax^7)^-1-(y^5)^-1)/((abx^6y^4)^-1+(b)^-1)#

Explanation:

#(1/(ax^8y)-1/(xy^6))/(1/(abx^7y^5)+1/(bxy))#

Multiply numerator and denominator by #xy#

#((xy)/(ax^8y)-(xy)/(xy^6))/((xy)/(abx^7y^5)+(xy)/(bxy))#

Cancel where possible:

#((cancel(x)cancel(y))/(ax^7cancel(y))-(cancel(x)cancel(y))/(cancel(x)y^5))/((cancel(x)cancel(y))/(abx^6y^4)+(cancel(x)cancel(y))/(bcancel(x)cancel(y)))=(1/(ax^7)-1/(y^5))/(1/(abx^6y^4)+1/b)#

#-> ((ax^7)^-1-(y^5)^-1)/((abx^6y^4)^-1+(b)^-1)#

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