If \(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}\) then which of the following are possible values of x?

Indicate all such values.

A. − 60

B. − 12

C. − 1

D. 1

E. 2

F. 5

Quick Approach to these type of Questions Solve for the Denominator = 0 and REJECT those values for 'x' as the Denominator can't be 0.

In this question x not equal to 2 & -12 AS IT WILL MAKE THE Denominator 0.

\(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}.......(5x^2 + 65x + 60)*(x-2)=(x^2 + 10x -24)*(5x+5).........5(x^2+13x+12)*(x-2)=(x^2 + 10x -24)*5(x+1).........(x+12)(x+1)*(x-2)=(x + 12)(x -2)*(x+1)\)
so LHS=RHS therefore all values of x are possible except when the denominator becomes 0....
1) x-2=0 means x=2
2) \(x^2 + 10x -24=0........x^2+12x-2x-24=0....(x+12)(x-2)=0\) so x can be 2 or -12
combined x should not be 2 and -12 and rest of the values are possible.
Thus A, C, D and F

also, x=-12 gives undefined value, so this is also not possible

Thanks. might be an oversight

Carcass , can you please explain the answer of the question. Thanks in advance.

Dear Sir the two explanations above (the short and the longest one ) are both perfect.

There is not a real shortcut

This problem makes no sense for me

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