How to divide the rational expressions ?
If A/B and C/D are rational expressions and B, C and D are non-zero then,
Step 1 :
If the given two rational expressions are in division, the first expression will be multiplied by the reciprocal of the second expression.
Step 2 :
Simplify the numerators and denominators in step 1.
Step 3 :
The result will be the lowest form if possible.
Note :
Sometimes it may be necessary to use factorization and algebraic identities.
Problem 1 :
Solution :
Keep the first fraction as it is, next change the division sign as multiplication and write the reciprocal of the second fraction.
After we did the possible simplification, the answer is 5/6.
Problem 2 :
Solution :
Keep the first fraction as it is, next change the division sign as multiplication and write the reciprocal of the second fraction.
After we did the possible simplification, the answer is 3.
Problem 3 :
Solution :
a^{2}-b^{2} = (a+b)(a-b)
Problem 4 :
Solution :
a^{2}-b^{2} = (a+b)(a-b)
x^{2}-7^{2} = (x+7)(x-7)
Problem 5 :
Solution :
Factoring 6 from, we get
6a+30 = 6(a+5)
Problem 6 :
Solution :
a^{2}-b^{2} = (a+b)(a-b)
x^{2}-64^{ }= x^{2}-8^{2} = (x+8)(x-8)
Problem 7 :
Solution :
Factoring 4, from c^{2}+4c, we get
c^{2}+4c = c(c+4)
c^{2}-c-20 = (c-5)(c+4)
Problem 8 :
Solution :
x^{2}+10x+21 = (x+3)(x+7)
x^{2}+5x+4 = (x+1)(x+4)
x^{2}+4x = x(x+4)
x^{3}+7x^{2} = x^{2}(x+7)
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