Please can someone help?
3/(x-7) + x^2+5x
My answer is:
x^3-2x^2-35x+3/(x-7)
Is this right? I converted x^2+5x so that it had a common denominator of x-7 so I could add them.
To determine if your answer is correct, let's simplify the expression step by step.
The given expression is:
3/(x-7) + x^2 + 5x
To combine the terms, we need a common denominator. The common denominator for the first term, 3/(x-7), and the second term, x^2 + 5x, is (x-7).
Let's rewrite the second term with a common denominator of (x-7):
(x^2 + 5x)(x-7)/(x-7)
Now we can combine the terms:
3/(x-7) + (x^2 + 5x)(x-7)/(x-7)
To add or subtract fractions, we need a common denominator. In this case, the common denominator is (x-7).
Applying the common denominator, we have:
3(x-7)/(x-7) + (x^2 + 5x)(x-7)/(x-7)
Now, let's simplify each term separately.
For the first term, 3(x-7)/(x-7), the (x-7) terms cancel out, resulting in:
3
For the second term, (x^2 + 5x)(x-7)/(x-7), we simplify it by distributing (x-7) into (x^2 + 5x):
(x^3 - 2x^2 - 35x) / (x-7)
Now, combining the simplified terms:
3 + (x^3 - 2x^2 - 35x) / (x-7)
So, based on the steps above, the simplified expression is:
x^3 - 2x^2 - 35x + 3 / (x - 7)
Therefore, your answer of x^3 - 2x^2 - 35x + 3 / (x - 7) is correct.