Simplify: (x+4)/(x+6) -(x-6)/(x+4). | Simplification of Rational Expressions | SciPiPupil

Simplify: $\dfrac{x-4}{x+6} - \dfrac{x-6}{x+4}$

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,

= $\dfrac{x-4}{x+6} - \dfrac{x-6}{x+4}$

= $\dfrac{x-4}{x+6}$ x $\dfrac{x+4}{x+4} -\dfrac{x-6}{x+4}$ x $\dfrac{x+6}{x+6}$

= $\dfrac{x^2-4^2}{(x+4)(x+6)} - \dfrac{x^2-6^2}{(x+4)(x+6)}$

= $\dfrac{x^2- 16}{(x+4)(x+6)} -\dfrac{x^2-36}{(x+4)(x+6)}$

= $\dfrac{x^2-16-(x^2-36)}{(x+4)(x+6)}$

= $\dfrac{x^2-16-x^2+36}{(x+4)(x+6)}$

= $\dfrac{20}{(x+4)(x+6)}$

= Answer

Explanation to the above answer.

Step 1: Copy the same question given.

Step 2: We need to make the denominators same to perform the subtraction. Therefore, we take the LCM of the two terms and do mathematics accordingly.

Step 3: Now, in the numerator, we have (a+b)(a-b) so, we write a²-b². This is the factor formula of (a²-b²). On the denominator, we write the expressions in factor form.

Step 4: We write the numeric value of b². 

Step 5: We subtract the two terms as they have like denominators. While subtracting, we write only one denominator. 

Step 6: As we had subtraction sign, we need to multiply the second term's expression by the '-' sign before we can perform further operations. So, we do this.

Step 7: Similar terms with opposite signs in the numerator gets added and result 0. The numbers are subtracted. And, we get the expression {20/(x+4)(x+6)} as our answer.

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Question: Simplify: (x+4)/(x+6) -(x-6)/(x+4). | Simplification of Rational Expressions | SciPiPupil

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