Addition of Rational Expressions |
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In previous lessons, you learned how to add and subtract rational expressions. We will now extend these concepts to slightly more difficult expressions.
For any two rational expressions p(x) /qx and r(x)/s(x) where q(x)≠ s(x), their sum is given by |
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and if q(x)=s(x)
that is, if the rational expressions are of the form p(x)/qx, r(x)/s(x) then |
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Example 1 |
| Find the sum of |
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2a2b≠100a3
We first find the LCM of the denominators.
2a2b=2∗a2∗b
100a3=22∗52∗a3
LCM=22∗52∗a3∗b
=100a3b |
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| we get |
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Example 2 |
| Find the value of |
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Example 3 |
| Find the sum of (x+2)/(x-2) and (x-2)/(x+2) |
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Try these questions |
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Answers to questions |
1. |
To solve |
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Consider q(x)=17x
s(x)=51x
=3∗17x
∴ LCM of q(x),s(x)=51x |
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2. |
To solve |
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Consider the denominators
p(x)=xy
s(x)=xy3
u(x)=x2y2
Irreducible factors x,y
Highest exponent of factors 2, 3
∴ LCM =x2y3
then
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3. |
To solve |
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a–x≠a+x |
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4. |
To solve |
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Let q(x)=x2–y2
s(x) =(x2+xy)
Factorizing
q(x) =(x–y)(x+y)
s(x)=x(x+y)
Irreducible factors are x, x+y, x–y
Highest exponents of these factors are 1, 1, 1
LCM=x(x+y)(x–y) |
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5. |
To solve |
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Factorizing the numerators and denominators |
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Canceling like terms in the numerator and denominator of each polynomial. |
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