5x-6/10x^2-7x-6
http://www.jiskha.com/display.cgi?id=1412542641
A good site for long division is ath calc101.com
Just click on the "long division" tab to see all the details, in proper formatting.
To simplify the rational expression 5x - (6/10x^2 - 7x - 6), we need to follow these steps:
Step 1: Simplify the numerator.
The numerator is simply 5x, so there is no simplification needed there.
Step 2: Simplify the denominator.
The denominator is 10x^2 - 7x - 6. To simplify it, we need to factor it.
The first step is to find two numbers whose product is equal to the product of the leading coefficient (10) and the constant term (-6) and whose sum is equal to the coefficient of the linear term (-7). In this case, the numbers are -10 and 1. So, we can rewrite the denominator as:
10x^2 - 10x + x - 6
Next, we group the terms and factor by grouping:
(10x^2 - 10x) + (x - 6)
10x(x - 1) + 1(x - 6)
10x(x - 1) + (x - 6)
Now, we have a common factor of (x - 1):
(x - 1)(10x + 1)
So, the simplified denominator is (x - 1)(10x + 1).
Step 3: Combine the simplified numerator and denominator.
Now, we can combine the simplified numerator (5x) and denominator ((x - 1)(10x + 1)) to get the final simplified expression:
5x / (x - 1)(10x + 1)
Therefore, the simplified rational expression is 5x / (x - 1)(10x + 1).