Simplify 2x2+4xy−3x−6y2x2+xy−6y2\dfrac{2x^2+4xy-3x-6y}{2x^2+xy-6y^2}. Answer ...

Factorisation quadraticFactorisation linearBrackets common factorsExpansion productsAdd subtract fractions中文
Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

3

1. Factorise the numerator by grouping.

2x2+4xy−3x−6y=2x(x+2y)−3(x+2y)=(x+2y)(2x−3)2x^2+4xy-3x-6y=2x(x+2y)-3(x+2y)=(x+2y)(2x-3)

2. Factorise the denominator as a quadratic expression.

2x2+xy−6y2=(2x−3y)(x+2y)2x^2+xy-6y^2=(2x-3y)(x+2y)

3. Cancel the common factor and write the simplified expression.

2x2+4xy−3x−6y2x2+xy−6y2=(x+2y)(2x−3)(2x−3y)(x+2y)=2x−32x−3y\frac{2x^2+4xy-3x-6y}{2x^2+xy-6y^2}=\frac{(x+2y)(2x-3)}{(2x-3y)(x+2y)}=\frac{2x-3}{2x-3y}

Answer

2x−3x−2y\dfrac{2x-3}{x-2y}

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

More questions on this topic

  1. 1The equation of a curve is y=x2e2xy = x^2 e^{2x}. Obtain an expression for dydx\dfrac{dy}{dx}. Find the range of values of xx…
  2. 2Factorise completely 9b2−6ab+a2−x29b^{2} - 6ab + a^{2} - x^{2}. Simplify 52x2−7x−4−84−x\dfrac{5}{2x^{2} - 7x - 4} - \dfrac{8}{4 - x}.
  3. 3Using factorisation, solve 9x2+6x−8=09x^2 + 6x - 8 = 0. Answer x = ... or ... Hence solve 9(y−1)2+6y−14=09(y-1)^2 + 6y - 14 = 0. Answer y = .…
  4. 4Factorise completely. abc−3c−6+2ababc - 3c - 6 + 2ab Answer ... 80x4−580x^{4} - 5 Answer ...
  5. 52x2−5xy−12y2x2−16y2\displaystyle \frac{2x^2-5xy-12y^2}{x^2-16y^2} Simplify. Answer ...