Simplify: 1/(a-b)(a-c) + 1/(c-b)(a-c) | Simplification of Rational Expressions | SciPiPupil

Simplify: $\frac{1}{(a-b)(b-c)} + \frac{1}{(c-b)(a-c)}$

This is a class 10 Question From Simplification of Rational Expressions chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the description below. If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. 

Solution:

Given,

= $\frac{1}{(a-b)(b-c)} + \frac{1}{(c-b)(a-c)}$

= $\frac{1}{(a-b)(b-c)} -\frac{1}{(b-c)(a-c)}$

= $\frac{1(a-c)}{(a-b)(b-c)(a-c)} -\frac{1(a-b)}{(a-b)(b-c)(a-c)}$

= $\frac{a-c -(a-b)}{(a-b)(b-c)(a-c)}$

= $\frac{a-c -a+b)}{(a-b)(b-c)(a-c)}$

= $\frac{(b-c)}{(a-b)(b-c)(a-c)}$

= $\frac{1}{(a-b)(a-c)}$

= Answer

Explanation to the above answer.

Step 1: Copy the same question given.

Step 2: We have most of the denominators in where the variables follow the alphabetical order. So, we take the '-' sign common in the second term and change the sign of one factor (c-b) into (b-c). 

Step 3: We take the LCM. And then, perform the required operations. 

Step 4: As the denominators are like now, we can subtract the two terms. 

Step 5: We multiply the second expression with a '-' sign in the numerator.

Step 6: Similar terms with opposite signs in the numerator gets added and result 0.  

Step 7: The common terms in the numerator and the denominator get divided and result 1. And, we re-write the remaining expression. And get our answer.

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Question: Simplify: 1/(a-b)(a-c) + 1/(c-b)(a-c) | Simplification of Rational Expressions | SciPiPupil

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