Question

simplify x^2 + ax - 2a^2÷
3a^2 - 2ax - x^2?
​

Answer 1

Answer:

$- \frac{x + 2a}{3a + x}$

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

$\frac{x(x + 2a) - a(x + 2a)}{a(3a + x) - x(3a + x)}$

vii) factor out x+2a from the expression

$\frac{(x + 2a)(x - a)}{a(3a + x) - x(3a + x)}$

viii) factor out 3a+x from the expression

$\frac{(x + 2a)(x - a)}{(3a + x)(a - x)}$

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

$\frac{(x + 2a)( - ( - a - x))}{(3a + x)(a - x)}$

x) reduce the fraction a-x

$\frac{(x + 2a)( - 1)}{(3a + x)}$

$- \frac{x + 2a}{3a + x}$