We need to calculate the simplified form of the expression, frac{c^{2} + 13c + 18}{c^{2} - 9} + frac{c + 1}{c + 3} - frac{c + 8}{c - 3}

Lewis Harvey

Lewis Harvey

Answered question

2021-01-22

We need to calculate the simplified form of the expression,
c2 + 13c + 18c2  9 + c + 1c + 3  c + 8c  3

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-01-23Added 105 answers

Given Information:
The given expression is c2 + 13c + 18c2  9 + c + 1c + 3  c + 8c  3
Formula:
The algebraic identity used is a2  b2=(a + b)(a  b).
Calculation:
Consider the expression, c2 + 13c + 18c2  9 + c + 1c + 3  c + 8c  3
First, factor the denominators of this expression and apply
a2  b2=(a + b)(a  b) in c2  9 as follows:
c2 + 13c + 18c2  9 + c + 1c + 3  c + 8c  3=c2 + 13c + 18(c  3)(c + 3) + c + 1c + 3  c + 8c  3
Now, consider the denominators, (c  3)(c + 3), c + 3 and c  3.
The least common denominator (LCD) is (c  3)(c + 3).
Now multiply the numerator and the denominator of c2 + 13c + 18(c  3)(c + 3) with 1, c + 1c + 3 with c  3 and c + 8c  3 with c + 3 to get the LCD in the denominator as follows:
c2 + 13c + 18(c  3)(c + 3) + c + 1c + 3  c + 8c  3= (c2 + 13c + 18)(1)(c  3)(c + 3)(1) + (c + 1)(c  3)(c + 3)(c  3)  (c + 8)(c + 3)(c  3)(c + 3)
=(c2 + 13c + 18)(1) + (c + 1)(c  3)  (c + 8)(c + 3)(c  3)(c + 3)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?