___3____ + ___5__

x-4 x-3
--------------------
-4 1
______ - ______
x-5 x-4

simplify the complex fraction

Did you see how your question looks?

Retype using brackets,
e.g.

(3/(x-4) + 5/(x-3) .... ) / ( ..............)

To simplify the given complex fraction, we can follow these steps:

Step 1: Simplify the numerator and denominator of the first fraction separately.
- The numerator is: -4(x-4) - 1(x-3)
Distribute: -4x + 16 - x + 3
Combine like terms: -5x + 19

- The denominator is: (x-5)(x-4)

Step 2: Simplify the numerator and denominator of the second fraction separately.
- The numerator is: -4(x-5) - 1(x-4)
Distribute: -4x + 20 - x + 4
Combine like terms: -5x + 24

- The denominator is: (x-4)

Step 3: Rewrite the complex fraction with the simplified numerator and denominator.
[(-5x + 19) / ((x-5)(x-4))] - [(-5x + 24) / (x-4)]

Step 4: Find a common denominator for the fractions.
Since both fractions have a denominator of (x-4), we can combine them by finding a common denominator.

Step 5: Combine the fractions.
[(-5x + 19) - (-5x + 24)] / (x-4)
Simplify the numerator: -5x + 19 + 5x - 24
Combine like terms: -5x + 5x - 5

Step 6: Finalize the simplified fraction.
The simplified complex fraction is -5 / (x-4).