(x-2) : (x+ 2) = (x +3) : (x + 11) then find value x

1.	(x-2) : (x+ 2) = (x +3) : (x + 11) then find value x
Answer» Step-by-step EXPLANATION: Given:- $\sf(<klux>X</klux> - 2) : (x + 2) = (x + 3) : (x + 11)$ To Find:- The value of x Solution:- $\sf(x - 2) : (x + 2) = (x + 3) : (x + 11)$ $\sf \implies \dfrac{x - 2}{x + 2} = \dfrac{x + 3}{x + 11}$ By cross multiplication:- $\sf \implies (x - 2)(x + 11)= (x + 3)(x + 2)$ $\sf \implies x(x + 11) - 2(x + 11)= x(x + 2) + 3(x + 2)$ $\sf \implies {x}^{2} + 11x - 2x - 22= {x}^{2} + 2x+ 3x + 6$ $\sf \implies {x}^{2} + 9x - 22= {x}^{2} + 5x + 6$ $\sf \implies {x}^{2} - {x}^{2} + 9x - 5x - 22 - 6 = 0$ $\sf \implies 4x - 28 = 0$ $\sf \implies 4x = 28$ $\sf \implies x = \dfrac{28}{4}$ $\sf \implies x = 7$ $\longrightarrow \underline{\boxed{\rm \therefore \: The \: value \: of \: x = 7 }}$ LET'S Check:- Substitute x = 7 in $\sf (x - 2)(x + 11)= (x + 3)(x + 2)$ $\sf \implies (7 - 2)(7 + 11)= (7 + 3)(7 + 2)$ $\sf \implies 5 \times 18 = 10 \times 9$ $\sf \implies 90 = 90$ LHS = RHS Hence Verified

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Step-by-step EXPLANATION: