Question

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Answer 1

Given:

The expression is:

$\dfrac{15m^2-3}{3m-1}$

To find:

The simplified value of the given expression.

Solution:

We have,

$\dfrac{15m^2-3}{3m-1}$

On dividing, we get

$(3m-1)|\overline{15m^2+0m-3}|5m+\dfrac{5}{3}$

          $-(15m^2-5m)$

              $\overline{\quad \quad -5m-3}$

                    $-(5m-\dfrac{5}{3})$

                       $\overline{\quad \quad -\dfrac{4}{3}}$

Here, quotient is $5m+\dfrac{5}{3}$  and the remainder is  $-\dfrac{4}{3}$.

Therefore, $\dfrac{15m^2-3}{3m-1}=5m+\dfrac{5}{3}-\dfrac{4}{3(3m-1)}$.