How do you simplify #\frac{\frac{25a^{2}-b^{2}}{ab}}{\frac{5a+b}{a}}#?

1 Answer
smendyka
Oct 31, 2017

See a solution process below:

Explanation:

First, use this rule for quadratics to factor the uppermost denominator:

#color(red)(x)^2 - color(blue)(y)^2 = (color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y))#

#(((5a + b)(5a - b))/(ab))/((5a + b)/a)#

Now, use this rule for dividing fractions to simplify the expression:

#(color(red)((5a + b)(5a - b))/color(blue)(ab))/(color(green)(5a + b)/color(purple)(a)) =>#

#(color(red)((5a + b)(5a - b)) xx color(purple)(a))/(color(blue)(ab) xx color(green)((5a + b))) =>#

#(color(red)(color(green)(cancel(color(red)((5a + b))))(5a - b)) xx color(blue)(cancel(color(purple)(a))))/(color(blue)(color(purple)(cancel(color(blue)(a)))b) xx color(red)(cancel(color(green)((5a + b))))) =>#

#(5a - b)/b#

Or

#(5a)/b - b/b => (5a)/b - 1#

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