Video Transcript
Simplify two 𝑥 over five plus
three 𝑥 over four.
In this question, we are asked to
simplify the sum of two fractions. Since these fractions involve an
unknown, 𝑥, we call these algebraic fractions. The techniques for adding algebraic
fractions together are very similar to adding regular fractions. We need their denominators to be
equal so that we can add them together by adding their numerators.
We can find that the lowest common
multiple of the denominators is 20. So, we want to rewrite both
fractions to have a denominator of 20. We can do this by multiplying the
first fraction by four over four and the second fraction by five over five, where we
can note that we are not changing the values in this expression since, in both
cases, we are multiplying by one.
We now calculate that two 𝑥 times
four is eight 𝑥 and three 𝑥 times five is 15𝑥. So, we are left with eight 𝑥 over
20 plus 15𝑥 over 20. Now that the denominators are
equal, we can add the algebraic fractions by adding the numerators. We get eight 𝑥 plus 15𝑥 all over
20. We now want to add the two terms in
the numerator. We see that these are like terms,
so we add their coefficients to obtain 23𝑥 over 20.
Finally, since we need to write our
answer in a simplified form, we need to check if there are any factors that we can
cancel. We note that the highest common
factor of 23 and 20 is one. So, we cannot simplify any
further. Hence, we were able to simplify two
𝑥 over five plus three 𝑥 over four to be 23𝑥 over 20.
