Question

(4 + x) (5 - x) / (2 + x) (7 - x) = 1​

Answer 1

$\huge\mathtt\red{Question}$

$→ \frac{(4 + x)(5 - x)}{(2 + x)(7 - x)} = 1$

$\huge\mathtt\red{Solution}$

$→ \frac{(4 + x)(5 - x)}{(2 + x)(7 - x)} = 1$

$→\frac{4(5 - x) + x(5 - x)}{2(7 - x) + x(7 - x)} = 1$

$→ \frac{20 - 4x + 5x - {x}^{2} }{14 - 2x + 7x - {x}^{2} } = 1$

$→\frac{20 + x - {x}^{2} }{14 + 5x - {x}^{2} } = 1$

$by \: cross \: multiplication \: we \: get$

$→20 + x - {x}^{2} = 14 + 5x - {x}^{2}$

$→20 - 14 + x - 5x - {x}^{2} + {x}^{2} = 0$

$→3 - 4x = 0$

$→ - 4x = - 3$

$→x = \frac{ 3}{4}$