Question : Simplify the given expression and find the value for $x=-1$.
$\frac{10 x^2+5 x+2 x y+y}{5 x+y}$
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2
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Correct Answer: –1
Solution :
Given: $\frac{10 x^2+5 x+2 x y+y}{5 x+y}$
$=\frac{5x(2x+1)+y(2x+1)}{5x+y}$
$=\frac{(5x+y)(2x+1)}{5x+y}$
$=2x+1$
$=2(-1)+1$ [since $x=-1$]
$=-1$
Hence, the correct answer is –1.
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