How do you simplify #\frac { 2x ^ { 2} + 5x y - 12y ^ { 2} } { 2x ^ { 2} + 9x y + 4y ^ { 2} }#?
2 Answers
This gives
Explanation:
Learn to factor trinomials. When you want to factor something like
Two numbers that multiply to
We will apply this to our problem now. Two numbers that multiply to
#2x^2 +5xy -12y^2 =2x^2 + 8xy - 3xy - 12y^2= 2x(x + 4y) - 3y(x + 4y) = (2x - 3y)(x + 4y)#
Now to the denominator. Two numbers that multiply to
#2x^2 + 9xy +4y^2 =2x^2 +8xy +xy + 4y^2 =2x(x + 4y) + y(x + 4y) = (2x + y)(x + 4y)#
Rewriting in fraction form:
#((2x - 3y)(x + 4y))/((2x + y)(x + 4y))#
#= (2x- 3y)/(2x +y)#
Hopefully this helps!
Explanation:
first factor the top equation to: