Simplification of Rational Expressions | SciPiPupil


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

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,

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

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

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

= $\frac{(2x-x^2-1) -6x+3 +x+2}{(x+2)(1-x)(2x-1)}$

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

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

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

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

= 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). Similarly, in the last term change the minus sign to addition sign and then change the denominator accordingly.

Step 3: We take the LCM of all the three terms as their denominators are the same.

Step 4: We perform basic mathematics here.

Step 5: We add and subtract in the numerator and get a new expression.

Step 6: We take the minus sign common in the numerator and re-write the expression.

Step 7: In the numerator, using mid-term factorization method, we find the factors of the expression. Then, as we had minus sign, we use this to change the denominator. - (1-x)  = x-1

Step 8: Same terms in the numerator and denominator get divided and result 1. Them, we write the remaining expression as answer.


Here is the Facebook link to the solution of this question in image. 

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

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

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