Question Video: Dividing Algebraic Expressions Mathematics

Video Transcript

Simplify 24 over 12 multiplied by 𝑛 plus five divided by 𝑛 plus three over 𝑛 plus five multiplied by 𝑛 plus three.

So, the first thing we do is remind ourselves of how we divide fractions. And to do that, what we have is 𝑎 over 𝑏 divided by 𝑐 over 𝑑 is equal to 𝑎 over 𝑏 multiplied by 𝑑 over 𝑐, so the reciprocal of the second fraction, which is equal to 𝑎𝑑 over 𝑏𝑐. So, what we’ve got here is two rational expressions, and we’re gonna divide them. So, using our rule for dividing fractions, what we’re gonna get is 24 over 12 multiplied by 𝑛 plus five multiplied by 𝑛 plus five multiplied by 𝑛 plus three over 𝑛 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 we’ve got 𝑛 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, we’ve got a common factor of 𝑛 plus three on the numerator and dominator. So first of all, we can divide through by 𝑛 plus five, which cancel these out, and then we can divide through by 𝑛 plus three. So now, what we can do is work out the result. But what we’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, we’ve got 24 over 12 multiplied by one, which is just equal to two.