1 answer

Which expression is equivalent to the following complex fraction?

Question:

enter image source here


Answers

See a solution process below:

Explanation:

We can use this rule for dividing fractions to simplify this expression:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

Substituting gives:

#(color(red)(x)/color(blue)(x - 3))/(color(green)(x^2)/color(purple)(x^2 - 9)) => (color(red)(x) xx color(purple)((x^2 - 9)))/(color(blue)((x - 3)) xx color(green)(x^2))#

We can factor #color(purple)((x^2 - 9)# as #color(purple)((x - 3))color(purple)((x + 3))# giving:

#(color(red)(x) xx color(purple)((x - 3))color(purple)((x + 3)))/(color(blue)((x - 3)) xx color(green)(x^2))#

We can now cancel common terms in the numerator and denominator giving:

#(cancel(color(red)(x)) xx cancel(color(purple)((x - 3)))color(purple)((x + 3)))/(cancel(color(blue)((x - 3))) xx cancel(color(green)(x^2))x) =>#

#(x + 3)/x# which is the third answer.

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