The solution of the equation [tex]\dfrac{3}{a+2}-\dfrac{6a}{a^2-4}=\dfrac{1}{a-2}[/tex] is (a = -2) and this can be determined by using the arithmetic operations.
Given :
Equation - [tex]\dfrac{3}{a+2}-\dfrac{6a}{a^2-4}=\dfrac{1}{a-2}[/tex]
The following steps can be used to evaluate the given equation:
Step 1 - Write the equation.
[tex]\dfrac{3}{a+2}-\dfrac{6a}{a^2-4}=\dfrac{1}{a-2}[/tex]
Step 2 - Rewrite the above equation.
[tex]\dfrac{3}{a+2}-\dfrac{1}{a-2}=\dfrac{6a}{a^2-4}[/tex]
Step 3 - Take the LCM.
[tex]\dfrac{3(a-2)-(a+2)}{a^2-2^2}=\dfrac{6a}{a^2-4}[/tex]
Step 4 - Further simplify the above expression.
[tex]\dfrac{3a-6-a-2}{a^2-4}=\dfrac{6a}{a^2-4}[/tex]
Step 5 - Cancel out the denominator of both sides and then further simplify.
2a - 8 = 6a
a = -2
For more information, refer to the link given below:
https://brainly.com/question/22122594
