Simplify: (2a-6)/(a²-9a+20) -(a-1)/(a²-7a+12) -(a-2)/(a²-8a+15). | Trigonometric Identities | SciPiPupil

Simplify: $\frac{2a-6}{a²-9a+20} - \frac{a-1}{a²-7a+12}-\frac{a-2}{a²-8a+15}$

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,

= $\frac{2a-6}{a²-9a+20} - \frac{a-1}{a²-7a+12}-\frac{a-2}{a²-8a+15}$

= $\frac{2a-6}{(a-4)(a-5)} - \frac{a-1}{(a-3)(a-4)}-\frac{a-2}{(a-3)(a-5)}$

= $\frac{2(a-3)(a-3) -(a-1)(a-5) -(a-2)(a-4)}{(a-3)(a-4)(a-5)}$

= $\frac{2(a²-6a+9) -(a²-6a+5) -(a²-6a+8)}{(a-3)(a-4)(a-5)}$

= $\frac{2a²-12a+18-a²+6a-5-a²+6a-8}{(a-3)(a-4)(a-5)}$

= $\frac{5}{(a-3)(a-4)(a-5)}$

= Answer

Explanation to the above answer.

Step 1: Copy the same question given.

Step 2: Use the mid-term factorization method to find the factors of the expressions given in the denominator.

Step 3: We take the LCM of all the three terms.

Step 4: We write the expression from the given factors.

Step 5: We multiply the expressions by the minus sign in the numerator and get a new expression.

Step 8: We add and subtract in the numerator and get the 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: (2a-6)/(a²-9a+20) -(a-1)/(a²-7a+12) -(a-2)/(a²-8a+15). | Trigonometric Identities | SciPiPupil

#SciPiPupil

#Simplification

#Algebra