Factorise x over 1 - x + 3 / x + 3/x= 5/1

Answer 1

To factorise the given equation, first combine the fractions on the left side:

x / (1 - x) + 3 / x + 3 / x = 5 / 1

Now find a common denominator for the fractions on the left side:

Common denominator = x(1 - x)

Rewrite the fractions with the common denominator:

x^2 / (x(1 - x)) + 3(1 - x) / (x(1 - x)) + 3(1 - x) / (x(1 - x)) = 5 / 1

Simplify the fractions with the common denominator:

x^2 + 3(1 - x) + 3(1 - x) = 5(x(1 - x))

Expand and simplify both sides:

x^2 + 3 - 3x + 3 - 3x = 5x - 5x^2

Combine like terms:

x^2 - 6x + 6 = 5x - 5x^2

Rearrange the equation and put it in standard form:

6x^2 - 11x + 6 = 0

Now factorise the equation:

(3x - 2)(2x - 3) = 0

Therefore, the factorised form of the equation is:

(3x - 2)(2x - 3) = 0