the denominator of fraction is 2 more than numerator. if 1 is subtracted from numerator and 1is added to denominator the fraction becomes 1/2 what is that fraction.

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[tex] \Large {\underline { \sf \orange{Clarification :}}}[/tex]

Here, as per the provided question we are given thatAlso,

the denominator of fraction is 2 more than numerator.if 1 is subtracted from numerator and 1is added to denominator the fraction becomes 1/2.We have to find the out original fraction.We’ll firstand

assume the numeratoranddenominatorastwo variables, sayxy. After that, we’ll form alinear equationand by solving that equation we’ll find thenumeratorand thedenominator.[tex] \Large {\underline { \sf \orange{Explication \: of \: Steps :}}}[/tex]

Let,

[tex] \maltese [/tex] Numerator = x

[tex] \maltese [/tex] Denominator = y

[tex]\bigstar \: \boxed{\sf { Fraction = \dfrac{x}{y} }} \\ [/tex]

Accordingtothequestion,[tex] \longrightarrow [/tex] Denominator = 2 + Numerator

[tex] \longrightarrow [/tex]

y = 2 + xLet it be the

equation(1).Also, as per the question,

[tex] \longrightarrow \sf { \dfrac{x-1}{y+1} = \dfrac{1}{2} } [/tex]

»Substituting the value ofyfrom theequation (1).[tex] \longrightarrow \sf { \dfrac{x-1}{2 + x+1} = \dfrac{1}{2} } [/tex]

[tex] \longrightarrow \sf { \dfrac{x-1}{3 + x} = \dfrac{1}{2} } [/tex]

Byusingcrossmultiplicationmethod,[tex] \longrightarrow \sf { 2(x-1) = 1(3+x) } [/tex]

Usingdistributiveproperty,[tex] \longrightarrow \sf { 2(x) + 2( -1) = 1(3) +1( x) } [/tex]

Performingmultiplication,[tex] \longrightarrow \sf { 2x – 2= 3 +x } [/tex]

Transposingvariablesandconstants,[tex] \longrightarrow \sf { 2x – x = 3 + 2 } [/tex]

Performingadditionandsubtraction,[tex] \longrightarrow \sf { x = 5 } [/tex]

[tex] \star \large {\bf{ Numerator = 5}} \star[/tex]

Findingoutthedenominator:Fromtheequation(1),wehave:[tex] \longrightarrow \sf { y = 2 + x } [/tex]

Substitutingthevalueofx,[tex] \longrightarrow \sf { y = 2 + 5 } [/tex]

[tex] \longrightarrow \sf { y = 7 } [/tex]

[tex] \star \large {\bf{ Denominator = 7}} \star[/tex]

[tex] \longrightarrow \\ [/tex] ❝ [tex] \boxed{ \sf \orange { Fraction = \dfrac{5}{7} }} \\[/tex] ❞

Therefore,thefractionis