Question

Solve:-

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

${ \rm{ \large{ \dfrac{(4 + x)(5 - x)}{ (2 + x)(7 - x)} = 1 }}}$

${ \rm{ \large{ { \implies(4 + x)(5 - x)} = 1.(2 + x)(7 - x) }}}$

${ \rm{ \large{ { \implies(4 + x)(5 - x)} = (2 + x)(7 - x) }}}$

${ \rm{ \large{ { \implies 20 - 4x + 5x- {x}^{2} } = 14 - 2x + 7x - {x}^{2} }}}$

${ \rm{ \large{ { \implies 20 + x- {x}^{2} } = 14 + 5x - {x}^{2} }}}$

${ \rm{ \large{ { \implies 20 + x- \not{x}^{2} } = 14 + 5x - \not {x}^{2} }}}$

${ \rm{ \large{ \implies 20 - 14 = 5x - x }}}$

${ \rm{ \large{ \implies 6= 4x }}}$

${ \rm{ \large{ \implies x= \dfrac{6}{4} }}}$

${ \rm{ \large{ \implies x= \dfrac{ { \not6}^{3} }{ { \not4}^{2} } }}}$

${ \rm{ \large{ \implies x= \dfrac{ {3} }{ ^{2} } }}}$

${ \rm{ \large{ \therefore x= \dfrac{ {3} }{ ^{2} } }}}$

Answer 2

$\huge\underline{\bf \red{ ❥ ᴀɴsᴡᴇʀ }}$

→ {(2+ x)(7− x)} / {(4+ x)(5− x)} =1

→ (4 +x)(5 −x) = 1.(2+ x)(7 −x)

→ (4+ x)(5 −x)= (2+ x)(7 −x)

→ 20 −4x+ 5x −x²

→ 14 −2x+ 7x− x²

→ 20+ x− x² = 14 +5x −x²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀↝ "x" is cancelled by another "x"

So,

→ 20 +x −2 = 14+ 5x −2

→ 20 −14 =5x− x

→ 6 = 4x

→ x = 6/4

→ x = 3/2

⠀⠀⠀⠀⠀↝ ∴ x = 3/2 Ans.