Question Video: Dividing Algebraic Expressions | Nagwa Question Video: Dividing Algebraic Expressions | Nagwa

# Question Video: Dividing Algebraic Expressions Mathematics

Simplify 24/(12(π + 5)) Γ· (π + 3)/((π + 5)(π + 3)).

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### Video Transcript

Simplify 24 over 12 multiplied by π plus five divided by π plus three over π plus five multiplied by π plus three.

So, the first thing we do is remind ourselves of how we divide fractions. And to do that, what we have is π over π divided by π over π is equal to π over π multiplied by π over π, so the reciprocal of the second fraction, which is equal to ππ over ππ. So, what weβve got here is two rational expressions, and weβre gonna divide them. So, using our rule for dividing fractions, what weβre gonna get is 24 over 12 multiplied by π plus five multiplied by π plus five multiplied by π plus three over π plus three.

So, in a problem like this, before we carry out any multiplying of numerators and denominators, what I like to do is see if we got any common factors that we can divide through by. But we can see that this is the case because weβve got π plus five is a common factor in the left-hand denominator and the right-hand numerator. And then if we look at the right-hand expression, weβve got a common factor of π plus three on the numerator and dominator. So first of all, we can divide through by π plus five, which cancel these out, and then we can divide through by π plus three. So now, what we can do is work out the result. But what weβre left with is 24 over 12 multiplied by one multiplied by one multiplied by one over one. Well, the right-hand expression is just one. So, weβve got 24 over 12 multiplied by one, which is just equal to two.

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