Simplification of Rational Expressions | SciPiPupil


Simplify: $\dfrac{p+2}{p-2} - \dfrac{p-2}{p+2}$

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,

= $\dfrac{p+2}{p-2} - \dfrac{p-2}{p+2}$

= $\dfrac{p+2}{p-2}$ x $\dfrac{p+2}{p+2}$ $-$ $\dfrac{p-2}{p+2}$ x $\dfrac{p-2}{p-2}$

= $\dfrac{(p+2)^2}{p^2-2^2} - \dfrac{(p-2)^2}{p^2-2^2}$

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

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

= $\dfrac{p^2+4p+4 -p^2+4p -4}{p^2-4}$

= $\dfrac{8p}{p^2-4}$

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, we have the like denominators in the form of (a+b)(a-b) = a²-b². 

Step 4: We subtract the given two terms. And write a single denominator.

Step 5: Now, we expand the formulae of (a+b)² = a²+2ab+b² and (a-b)² = a²-2ab+b².

Step 6: Remember, whenever we have a subtraction sign before any terms, the sign changes. So, we multiply the expanded form of (a-b)² by '-' sign. 

Step 7: Similar terms with opposite signs in the numerator gets added and result 0. And, we get the remaining expression as our answer.


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Question: Simplify: (p+2)/(p-2) - (p-2)/(p+2). | Simplification of Rational Expressions | SciPiPupil

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