what is the common denominator of 5/x^2-4 - 2/x+2 in the complex fraction 2/x-2 - 3/x^2-4 divided by 5/x^2-4 - 2/x+2A) (x + 2)(x - 2)B) x - 2C) (x + 2)^2(x - 2)D) x + 2
Accepted Solution
A:
Answer: A) (x + 2)(x - 2)
Step-by-step explanation:The given complex fraction is [tex]\Rightarrow\frac{\frac{2}{(x-2)}-\frac{3}{x^2-4} }{\frac{5}{(x^2-4)}-\frac{2}{x+2}}\\\\\text{Using identity, }a^2-b^2=(a+b)(a-b)\\\\\Rightarrow\frac{\frac{2}{(x-2)}-\frac{3}{(x-2)(x+2)}}{\frac{5}{(x-2)(x+2)}-\frac{2}{x+2}}\\\\\text{Taking LCM, we get}\\\\\Rightarrow \frac{\frac{2(x+2)-3}{(x-2)(x+2)\leftarrow same }}{\frac{5-2(x-2)}{(x+2)(x-2)\leftarrow same}}[/tex]Thus we can see that the common denominator in the above complex fraction is A) (x + 2)(x - 2)