Question

Simplify: 2x²+6x-8 from 3x?-4x+1​

Answer 1

Answer:

you need a common denominator on the left hand side which you get by multiplying the two together

$(4x^2 + 3x + 8)(4x^2 -6x + 8) = 2(4x^2 + 3x +8)(2x^2 - 3x + 4)$

the two numerator terms are each multiplied by the denominator of the other part of the equation to give

$2x(4x^2 - 6x + 8) + 3x(4x^2 - 6x + 8)$

then multiply out then collect together like terms and simplify

$(8x^3 - 12 x^2 + 16x) + (12 x^3 - 18x^2 + 24x)</p><p></p><p>= 20x^3 - 30x^2 + 40x</p><p></p><p>$

then factorise common factors out

$= 10x ( x^2 -3x +4)$

the desired total is 1/6 which means we equate the numerator to 1 and the denominator to 6 and have two equations that can be solved simulataneously numerator

$20x^3 - 30x^2 + 40x = 1$

equate to zero gives

$2(4x^2 + 3x +8)(2x^2 - 3x +4) = 6$

multiply out and equate to zero then solve the two equations simultaneously to get your values for x