Simplify Complex fraction:
(x-1)
-----
(x-3)
---------
1 4
---- - ----
x2-x-6 (x+2)
If you mean
(x-1)/(x-3) / (1/(x^2-x-6) - 4/(x+2)) then that is
(x-1)/(x-3) / (1 - 4(x-3))/((x-3)(x+2))
(x-1)/(x-3) * (x-3)(x+2) / (13-4x)
(x-1)(x+2)/(13-4x)
To simplify the complex fraction, you can follow these steps:
Step 1: Simplify the numerator and denominator of the fractional part of the complex fraction.
To simplify the numerator, factorize the quadratic expression x^2 - x - 6:
x^2 - x - 6 = (x - 3)(x + 2)
Now, the numerator becomes (x - 1) / (x - 3) / [(x - 3)(x + 2)].
Step 2: Invert the denominator of the fractional part and multiply it with the numerator.
Invert the denominator (x - 3)(x + 2) to get (1 / [(x - 3)(x + 2)]).
Now, the complex fraction becomes [(x - 1) / (x - 3)] * [(x + 2) / (x^2 - x - 6)].
Step 3: Simplify the complex fraction by canceling out the common factors.
Cancel out the common factor (x - 3) in the numerator and denominator:
[(x - 1) / (x - 3)] * [(x + 2) / (x^2 - x - 6)] = (x + 2) / (x^2 - x - 6).
This is the simplified form of the complex fraction.