Express as a single fraction in its simplest form: $\dfrac{x-1}{2x^2+x-3}-\dfrac{x+2}{2x^2+3x-2}$.

Question

Express as a single fraction in its simplest form: $\dfrac{x-1}{2x^2+x-3}-\dfrac{x+2}{2x^2+3x-2}$. State the restrictions on the original expression.

Accepted Answer

$- \dfrac{4}{\left(2 x - 1\right) \left(2 x + 3\right)}$ where $x - 1\ne0,\ 2 x + 3\ne0,\ x + 2\ne0,\ 2 x - 1\ne0$

Simplifying multi-term fractions