The given expression is:
[tex] \frac{4 x^{2} +10x-6}{2x-1} [/tex]
In order to simplify the expression we need to factorize the numerator, as shown below:
[tex] \frac{4 x^{2} +12x-2x-6}{2x-1} \\ \\
= \frac{4x(x+3)-2(x+3)}{2x-1} \\ \\
= \frac{(4x-2)(x+3)}{2x-1} \\ \\
= \frac{2(2x-1)(x+3)}{2x-1} \\ \\
=2(x+3)[/tex]
Thus, the simplified form of the expression is 2(x+3)
