Question

Simplify x^2 + ax - 2a^2÷
3a^2 - 2ax - x^2?
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Answer 1

`- (x + 2a)/(3a + x)`

Step-by-step explanation:

`\frac{ {x + ax - 2 {a}}^(2) }{3a {}^(2) - 2ax - {x}^(2) }`

i) write ax as a difference

`\frac{ {x}^(2) + 2ax - ax - 2 {a}^(2) }{3 {a}^(2) - 2ax - x {}^(2) }`

ii) write -2ax as a difference

`\frac{ {x}^(2) + 2ax - ax - 2a {}^(2) }{3a {}^(2) + ax - 3ax - x {}^(2) }`

iii) factor out x from the expression

`\frac{x(x + 2a) - ax - 2 {a}^(2) }{3 {a}^(2) + ax - 3ax - {x}^(2) }`

iv) factor out -a from the expression

`\frac{x(x + 2a) - a(x + 2a)}{3 {a}^(2) + ax - 3ax - {x}^(2) }`

v) factor out a from the expression

`\frac{x(x + 2a) - a(x + 2a)}{a(3a + x) - 3ax - {x}^(2) }`

vi) factor out -x from the expression

`(x(x + 2a) - a(x + 2a))/(a(3a + x) - x(3a + x))`

vii) factor out x+2a from the expression

`((x + 2a)(x - a))/(a(3a + x) - x(3a + x))`

viii) factor out 3a+x from the expression

`((x + 2a)(x - a))/((3a + x)(a - x))`

ix) factor out the negative sign from the expression and rearrange the term

`((x + 2a)( - ( - a - x)))/((3a + x)(a - x))`

x) reduce the fraction a-x

`((x + 2a)( - 1))/((3a + x))`

`- (x + 2a)/(3a + x)`