How do you simplify \frac { 2x ^ { 2} + 5x y - 12y ^ { 2} } { 2x ^ { 2} + 9x y + 4y ^ { 2} }?

2 Answers
Jan 24, 2018

This gives (2x - 3y)/(2x + y)

Explanation:

Learn to factor trinomials. When you want to factor something like 2x^2 -7x + 5, you want to find two numbers that multiply to the coefficients of the highest and lowest degree term and add to the middle degree term.

Two numbers that multiply to +10 and add to -7 are -5 and -2. Therefore, 2x^2 - 7x + 5 = 2x^2 - 2x - 5x + 5 = 2x(x - 1) - 5(x - 1) = (2x- 5)(x - 1)

We will apply this to our problem now. Two numbers that multiply to -24 and add to +5 would be +8 and -3. Thus:

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 8 and add to 9 would be +8 and +1.

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!

Jan 24, 2018

(​2x−3y)/(2x-y)​

Explanation:

first factor the top equation to: 2x^2-3xy+8xy-12y^2 then group then and and factor out to get: (x+4y)(2x-3y) then do the same for the second equation and you'll get: (2x+y)(x+4y) notice that the two equation both have (x+4y) in common and so they cancel each other out. so you'll let with your answer