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

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Answer 1 · 2018-01-09T13:36:09

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

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

#a^2-b^2 = (a+b)(a-b)#

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.

#(3m^2-4n^2)/(2m^2-n^2)# can be simplified by factorising to:

#((sqrt(3)m-2n)(sqrt(3)m+2n))/((sqrt(2)m+n)(sqrt(3)m-n))#

This is the simplest form.