The following steps would be useful to understand how to divide a rational expression by another rational expression.
Step 1 :
Write the first rational expression as it is. Change the division to multiplication and take reciprocal of the second rational expression.
Step 2 :
Factor both numerator and denominator, if possible.
Step 3 :
Identify the common factor at both numerator and denominator.
Step 4 :
The common factor identified at both numerator and denominator should be multiplied by the other terms.
Step 5 :
Now, get rid of the common factor at both numerator and denominator.
Example 1 :
Simplify :
Solution :
2a^{2 }+ 5a + 3 = (a + 1)(2a + 3)
2a^{2 }+ 7a + 6 = (2a + 3)(a + 2)
a^{2 }+ 6a + 5 = (a + 1)(a + 5)
-5a^{2 }- 35a - 50 = -5(a^{2} + 7a + 10) = -5(a + 2)(a + 5)
Example 2 :
Simplify :
Solution :
b^{2} + 3b - 28 = (b - 4)(b + 7)
b^{2} + 4b + 4 = (b + 2)(b + 2)
b^{2} - 49 = b^{2} - 7^{2} = (b - 7)(b + 7)
b^{2} - 5b - 14 = (b - 7)(b + 2)
Example 3 :
Simplify :
Solution :
Example 4 :
Simplify :
Solution :
12t^{2} - 22t + 8 = 2(6t^{2} - 11t + 4) = 2(3t - 4)(2t - 1)
3t^{2} + 2t - 8 = (t + 2)(3t - 4)
2t^{2 }+ 4t = 2t(t + 2)
Example 5 :
Find the value of x^{2}y^{-2}.
Solution :
Example 6 :
If a polynomial p(x) = x^{2} - 5x - 14 is divided by another polynomial q(x), we get (x - 7)/(x + 2). Find q (x).
Solution :
Take reciprocal on both sides.
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