Question

3. Find x for the equation: (2 + x)(7 – x)/(5 – x)(4 + x) = 1

Answer 1

Hey Pretty Stranger!

$\sf \dag \: \: \: \: \: \dfrac{(2 + x)(7 - x)}{(5 - x)(4 + x)} = 1$

$\hookrightarrow \sf \: \dfrac{2(7 - x) + x( 7- x)}{5(4 + x) - x(4 + x)} = 1$

$\hookrightarrow \sf \: \dfrac{14 - 2x + 7x - {x}^{2} }{20 + 5x - 4x - {x}^{2} } = 1$

$\hookrightarrow \sf \: \dfrac{14 + 5x - {x}^{2} }{20 +x - {x}^{2} } = 1$

$\hookrightarrow \sf \: 14 + 5x - {x}^{2} = 20 + x - {x}^{2}$

$\hookrightarrow \sf \: 5x - {x}^{2} - x + {x}^{2} = 20 - 14$

$\hookrightarrow \sf \: 4x = 6$

$\hookrightarrow \sf \: x = \dfrac{6}{4}$

$\hookrightarrow \large \boxed{ \purple{ \sf \: x = 1.5 }}$

Answer 2

HELLO FRIEND.......... HERE YOU GO..........

Answer:

x = 1.5

Step-by-step explanation:

(2 + x)(7 – x) ÷ (5 – x)(4 + x) = 1

14-2x+7x-x² ÷ 20+5x-4x-x² = 1

14-2x+7x-x² = 20+5x-4x-x²

-x²+5x+14 = -x²+x+20

             0 = -x²+x²+x-5x+20-14

             0 = -4x+6

            4x = 6

              x = 6÷4

              x = 3÷2

              x = 1.5

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