Question
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Tutor-Verified Answer
Answer
The simplified expression is
.
Solution
Calculate or simplify the expression
.
Simplify the expression by following steps:
Simplify the expression by following steps:
- step0: Solution:
- step1: Remove the parentheses:
- step2: Factor the expression:
- step3: Reduce fractions to a common denominator:
- step4: Rewrite the expression:
- step5: Transform the expression:
- step6: Multiply the terms:
- step7: Multiply the terms:
- step8: Subtract the terms:
- step9: Calculate:
The simplified expression is.
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Beyond the Answer
To simplify the expression
we first need to factor the denominators.
-
Factor the Denominators:For
, we can look for factors using the Rational Root Theorem or by polynomial long division. By trying possible rational roots, we find is a root, which gives us Thus,For, we also find is a root, leading to So, -
Rewrite the Original Expression:Now we can rewrite the expression as:
-
Finding a Common Denominator:The common denominator is
. -
Rewrite each fraction to have this common denominator:
-
Combine the Numerators:
-
Simplify the Numerator:Expanding the first term:Expanding the second term:Now combine:
-
Final Expression:We now haveFactoring
from the numerator:
Thus, the simplified form of the expression is: