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 2021-01-22 Answered
We need to calculate the simplified form of the expression,
c2 + 13c + 18c2  9 + c + 1c + 3  c + 8c  3
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Expert Answer

mhalmantus
Answered 2021-01-23 Author has 106 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)

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