# How do you simplify \frac { 3m ^ { 2} - 4n ^ { 2} } { 2m ^ { 2} - n ^ { 2} } ?

Jan 9, 2018

What we must use is the difference of two squares, using roots instead of square numbers.

#### Explanation:

From our normal factorising, we must first not the use of D.O.T.S

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

However, it must noted we don't have whole square numbers as coefficients, therefore these will simply remain as roots.

It should also be noted that $\sqrt{{m}^{2}} = m$
The same applies for $n$ , lets factorise and simplify.

$\frac{3 {m}^{2} - 4 {n}^{2}}{2 {m}^{2} - {n}^{2}}$ can be simplified by factorising to:

$\frac{\left(\sqrt{3} m - 2 n\right) \left(\sqrt{3} m + 2 n\right)}{\left(\sqrt{2} m + n\right) \left(\sqrt{3} m - n\right)}$

This is the simplest form.