Question

Which expression is equivalent to 2a+1/10a-5 / 10a/4a^2-1

Answer 1

Answer: The answer is D

Step-by-step explanation: got it right 2023 edge

Answer 2

`\large\boxed{((2a+1)^2)/(50a)}`

Explanation:

`10a-5=5(2a-1)\\\\4a^2-1=2^2a^2-1^2=(2a)^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2a-1)(2a+1)\\\\(2a+1)/(10a-5)/(10a)/(4a^2-1)=(2a+1)/(5(2a-1))/(10a)/((2a-1)(2a+1))\\\\=(2a+1)/(5(2a-1))\cdot((2a-1)(2a+1))/(10a)\qquad\text{cancel}\ (2a-1)\\\\=(2a+1)/(5)\cdot(2a+1)/(10a)=((2a+1)^2)/(50a)`