On this page, you will learn completely about the rule of separation of division of algebraic fractions. Get to see the solved example questions in the coming sections of this article. Solved Examples on Separation of Division of Algebraic Fractions will make you familiar with the concept in a better way and you can solve related problems easily.
Rule of Separation of Division
- (x + y) / z = x/z + y/z
- (x – y) / z = x/z – y/z
- z / (x + y) ≠ z/x + z/y
From the above three expressions, we can observe that the denominator of the fractions should be the same to perform addition or subtraction operator between them. The rule of separation of division says that to calculate sum or difference between two or more fractions, you need to make a common denominator for them and add or subtract numerators.
Examples on Separation of Division of Algebraic Fractions
Example 1.
Find the difference of fractions by taking the common denominator: x / bc – y / ab?
Solution:
We observe the two denominators are bc and ab and their L.C.M. is abc. So, abc is the least quantity which is divisible by ab and bc. To subtract those fractions, you must make a common denominator i.e abc. To make denominator as abc for x / bc multiply it with a, and multiply y / ab with c.
Therefore, we can write
(x * a) / abc – (y * c) / abc
= (ax + cy) / abc
Example 2.
Find the sum of fractions by taking the common denominator: a / xy + b / xz + c / yz.
Solution:
There are three denominators xy, xz, and yz, and their L.C.M. is xyz. To make the fractions with the common denominator, the numerator and denominator of these are to be multiplied by xyz ÷ xy = z in case of a/xy, xyz ÷ yz = x in case of c/yz, xyz ÷ xz = y in case of b/xz.
Therefore, we can write
a / xy + b / xz + c / yz
= (a.z) / xyz + (b.y) / xyz + (c.x) / xyz
= (az + by + cx) / xyz
Example 3.
Solve fractions p/qr + q/pr – r/pq by taking the common denominator.
Solution:
We can observe that three fractions have denominators as qr, pr, and pq their L.C.M is pqr. To make a common denominator for three fractions, their numerators should be multiplied by pqr ÷ qr = p for p/qr, pqr ÷ pr = q for q/pr, and pqr ÷ pq = r for r/pq.
Therefore, we can write
p/qr + q/pr – r/pq
= (p.p) / pqr + (q.q) / pqr – (r.r) / pqr
= (p² + q² – r²) / pqr.
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