Video Transcript
Simplify two over three 𝑥 minus
one over five 𝑥.
In this question, we are asked to
simplify the difference between two fractions. Since the fractions contain an
unknown 𝑥, we call these algebraic fractions. We treat algebraic fractions in a
very similar way to normal fractions. We want to rewrite both fractions
to have the same denominator so that we can evaluate this difference by subtracting
the numerators. Therefore, we want to rewrite both
fractions to have the same denominator.
We see that both fractions already
have a factor of 𝑥 in the denominator. However, the coefficients of 𝑥 are
different. We can calculate that the lowest
common multiple of three and five is 15. This means that we can find
equivalent fractions to each fraction with a denominator of 15𝑥. We multiply the first fraction by
five over five and the second fraction by three over three.
It is worth reiterating at this
point that we are not changing the value of our expression since we are multiplying
each fraction by one. We multiply fractions together by
multiplying their numerators and denominators separately. We have two over three 𝑥 times
five over five is 10 over 15𝑥 and one over five 𝑥 times three over three is three
over 15𝑥.
We now need to find the difference
between the two fractions with the same denominator. We do this by finding the
difference between their numerators. We obtain 10 minus three all over
15𝑥. We then evaluate this difference to
get seven over 15𝑥. We note that there are no shared
factors other than one in the numerator and denominator. So, we cannot simplify any
further.
Hence, we have shown that two over
three 𝑥 minus one over five 𝑥 simplifies to give seven over 15𝑥.
