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04 - 22- 23
ALGEBRA: Division of Algebraic Expressions
(Sample Problems & Solutions) - Part 007
- Find the quotient of the following: ๐ โ 1 ๐ 2 + 1 รท ๐ โ 1 ๐ + 1 (^). Solution: Rewrite the expressions as follows, ๐ โ 1 ๐^2 + 1 รท ๐ โ 1 ๐ + 1 = ๐ โ 1 ๐^2 + 1 ๐ โ 1 ๐ + 1 Simplifying the expressions, cancel out ๐ โ 1 , since theyโre both present in the numerator and denominator, so we have, ๐ โ ๐ ๐^2 + 1 ๐ โ ๐ ๐ + 1 = ๐๐^ + ๐ ๐ + ๐ Therefore, the quotient of the given problem is ๐๐+๐ ๐+๐ .
- Simplify the following: ๐ ๐โ 1 ๐ 2 + ๐^4 ๐โ 1 2
Solution: ๐ ๐ โ 1 ๐^2 + 1 ๐ 4 ๐ โ 1 2 Rewrite the expressions as follows, ๐ ๐ โ 1 ๐^2 + 1 ๐ 4 ๐ โ 1 2
๐ ๐^ โ^1 ๐
๐ โ ๐^3 โ ๐ โ 1 โ ๐ โ 1
Cancel out the expressions that has common on both numerator and denominator, as follows, ๐ โ ๐ โ ๐ (^) โ ๐^2 + 1 ๐ โ ๐^3 โ ๐ โ ๐ โ ๐ โ 1 ๐ 2
- 1 ๐ 3 ๐ โ 1 or ๐ ๐
- ๐ ๐ ๐ โ ๐ ๐ Therefore, simplifying further the given problem, the result is ๐๐+๐ ๐ ๐ โ๐ ๐.
- Find the quotient of the following: ๐^2 โ 1 2 ๐ ๐+
รท
๐ ๐^2 โ 1 ๐+
Solution: ๐ 2 โ 1 2 ๐ ๐ + 1
รท
2 โ 1 ๐ + 1 2 Take the reciprocal of the second term, then proceed to multiplication, so we have, ๐ 2 โ 1 2 ๐ ๐ + 1
รท
2 โ 1 ๐ + 1 2
4 ๐ + 1
รท
๐ ๐ + ๐ ๐ ๐ 4 ๐ + 1
ร
๐ ๐ ๐ Rewrite the expressions for further simplification as follows, ๐^4 ๐ + 1
ร
3 ๐ 3 โ ๐ ๐ + 1
ร
3 Then cancel out some expressions, such as, ๐๐^ โ ๐ ๐ + ๐
ร
๐ ๐ ๐ + ๐ Therefore, the quotient of the given problem is ๐ ๐ + ๐.
- Find the quotient of the following: ๐^3 ๐^2 โ 1 2 ๐+
รท
๐+ 4 ๐ 4 ๐^2 โ 1
Solution: ๐^3 ๐^2 โ 1 2 ๐ + 1
รท
๐ + 1 4 ๐^4
2 โ 1 Take the reciprocal of the second term, then proceed to multiplication, so we have,
3 ๐ 2 โ 1 2 ๐ + 1
รท
๐ ๐ ๐ ๐ ๐ โ ๐ ๐ 3 ๐ 2 โ 1 2 ๐ + 1
ร
๐ โ ๐ ๐ + ๐ ๐ ๐ ๐ Rewrite the expressions for further simplification as follows, ๐ 3 ๐ 2 โ 1 2 ๐ + 1
ร
2 โ 1 ๐ + 1 4 ๐ 4 ๐๐^ ๐^2 โ 1 2 ๐ + 1
ร
๐ + 1 4 ๐๐^ โ ๐
Then cancel out some expressions, such as, ๐๐^ ๐^2 โ 1 2 ๐ + 1
ร
๐^2 โ 1
4 ๐ ๐ โ ๐ ๐ 2 โ 1 2 ๐ + 1
ร
2 โ 1 ๐ + 1 4 ๐ ๐ ๐ โ ๐ ๐ ๐ ๐ + ๐ ๐ Therefore, the quotient of the given problem is ๐ ๐ โ๐ ๐ ๐ ๐+๐ ๐ . RSM
