Question

How do you combine \[\dfrac{6y+5}{5y-25}-\dfrac{y+2}{y-5}\]?

Answer 1

Hint: In this problem, we have to combine the given two fractions by subtracting it. We can see that the denominator of the two fractions are not the same. We know that the denominator should be equal to perform addition or subtraction in it. We can now multiply 5 on both the numerator and the denominator to the second fraction, in order to get a similar denominator as the first fraction. We can then simplify the remaining terms to get the answer.

Complete step by step answer:
We know that the given fraction to be combined is,
\[\dfrac{6y+5}{5y-25}-\dfrac{y+2}{y-5}\]
We can see that the denominators are not similar.
We can now multiply 5 to the second fraction on both the numerator and the denominator, we get
\[\begin{align}
  & \Rightarrow \dfrac{6y+5}{5y-25}-\dfrac{y+2}{y-5}\times \dfrac{5}{5} \\
 & \Rightarrow \dfrac{6y+5}{5y-25}-\dfrac{5y+10}{5y-25} \\
\end{align}\]
Now we have similar denominators and hence we can simplify the above step, we get
\[\begin{align}
  & \Rightarrow \dfrac{6y+5-5y-10}{5y-25} \\
 & \Rightarrow \dfrac{y-5}{5y-25} \\
\end{align}\]
We can now take the common term 5 outside from the denominator, we get
\[\Rightarrow \dfrac{y-5}{5\left( y-5 \right)}\]
We can see that there is a similar factor in both the numerator and the denominator, so we can cancel them, we get
\[\Rightarrow \dfrac{1}{5}=0.2\]

Therefore, the answer is \[0.2\].

Note: Students make mistakes while subtracting two fractions with different denominators. We should always remember that the denominator should be the same to add or subtract the fraction. If it is not the same, we can multiply or divide by the required number in order to get similar denominators to perform addition or subtraction.