Given:
The expression is:
[tex]\dfrac{15m^2-3}{3m-1}[/tex]
To find:
The simplified value of the given expression.
Solution:
We have,
[tex]\dfrac{15m^2-3}{3m-1}[/tex]
On dividing, we get
[tex](3m-1)|\overline{15m^2+0m-3}|5m+\dfrac{5}{3}[/tex]
[tex]-(15m^2-5m)[/tex]
[tex]\overline{\quad \quad -5m-3}[/tex]
[tex]-(5m-\dfrac{5}{3})[/tex]
[tex]\overline{\quad \quad -\dfrac{4}{3}}[/tex]
Here, quotient is [tex]5m+\dfrac{5}{3}[/tex] and the remainder is [tex]-\dfrac{4}{3}[/tex].
Therefore, [tex]\dfrac{15m^2-3}{3m-1}=5m+\dfrac{5}{3}-\dfrac{4}{3(3m-1)}[/tex].
