Question

Subtract the rational expressions: (-9x²)/(x-5) - (25-10x²)/(x-5).

Answer 1

To subtract the rational expressions, simplify each expression and then combine them. In this case, the expression simplifies to x² - 25.

Step-by-step explanation:

To subtract the rational expressions, (-9x²)/(x-5) - (25-10x²)/(x-5), we need to simplify each expression and then combine them

Let's simplify the expressions:

First expression:

We can rewrite (-9x²)/(x-5) as (-9x²)/(1*(x-5)) and then cancel out the common factor (x-5). This leaves us with -9x².

Second expression:

We can rewrite (25-10x²)/(x-5) as (1*(25-10x²))/(1*(x-5)) and then cancel out the common factor (x-5). This leaves us with (25-10x²).

Now we can subtract the simplified expressions: -9x² - (25-10x²).

To subtract the expressions, we distribute the negative sign to each term in the second expression and then combine like terms:

-9x² - (25-10x²) = -9x² - 25 + 10x² = (10x² - 9x²) - 25 = x² - 25.