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Simplify: $\frac{1}{(x-3)(x+2)} + \frac{3}{(x+2)(4-x)}+\frac{2}{(x-3)(x-4)}$

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,

= $\frac{1}{(x-3)(x+2)} + \frac{3}{(x+2)(4-x)}+\frac{2}{(x-3)(x-4)}$

= $\frac{1}{(x-3)(x+2)} - \frac{$}{(x+2)(x-4)}+\frac{2}{(x-3)(x-4)}$

= $\frac{1(x-4) -3(x-3) +2(x+2)}{(x+2)(x-3)(x-4)}$

= $\frac{x-4-3x+9+2x+4}{(x+2)(x-3)(x-4)}$

= $\frac{9}{(x+2)(x-3)(x-4)}$

= Answer


Explanation to the above answer.


Step 1: Copy the same question given.

Step 2: We have most of the denominators 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 of all the three terms as their denominators are the same.

Step 4: Similar terms with opposite signs in the numerator gets added and result 0. Similarly, we perform the basic mathematics and get our answers. 


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Here is the Website link to the guide of Simplification of Rational Expressions.


Question: Simplify: 1/(x-3)(x+2) + 3/(x+2)(4-x) + 2/(x-3)(x-4) | Simplification of Rational Expressions | SciPiPupil

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