Question

(4х-24)/(х-5)+(х-9)/(5-х)

Answer 1

$\frac{4x-24}{x-5}+\frac{x-9}{5-x}=\frac{4x-24}{x-5}-\frac{x-9}{x-5}=\frac{4x-24-x+9}{x-5}= \frac{3x-15}{x-5}=\\\\\frac{3(x-5)}{x-5}=3$

Answer 2

To simplify the expression (4x-24)/(x-5) + (x-9)/(5-x), we need to find a common denominator for the two fractions and then combine them.

Step 1: Factor out -1 from the second fraction to make the common denominator positive: (4x-24)/(x-5) - (x-9)/(x-5)

Step 2: Now, we have the same denominator (x-5) for both fractions. We can combine the numerators: [(4x - 24) - (x - 9)] / (x - 5)

Step 3: Simplify the numerators: (4x - 24 - x + 9) / (x - 5)

Step 4: Combine like terms in the numerator: (3x - 15) / (x - 5)

Step 5: Factor out the common factor from the numerator: 3(x - 5) / (x - 5)

Step 6: Cancel out the common factor (x - 5) from the numerator and denominator: 3

So, the simplified expression is 3.