Math, asked by ssshhhh47, 8 months ago

X-1/x-2+x-3/x-4=3 1/3,x solve this ​

Answers

Answered by Anonymous
14

\;\;\underline{\textbf{\textsf{ Given  :-}}}

 \sf Equation\\{\sf{  \frac{x - 1}{x - 2}  +  \frac{x - 3}{x - 4} = \frac{10}{3}   }} \\ \\

\;\;\underline{\textbf{\textsf{ To Find   :-}}}

 \sf Value \: of \: x

\;\;\underline{\textbf{\textsf{ Solution  :-}}}

 \sf Given  \: that

 \\{\sf{  \frac{x - 1}{x - 2}  +  \frac{x - 3}{x - 4} = \frac{10}{3}   }} \\ \\

 \sf Then

  \longrightarrow {\sf{  \frac{(x - 1)(x - 3) + (x - 3)(x - 2)}{(x - 2)(x - 4)}  =  \frac{10}{3} }} \\ \\

  \longrightarrow {\sf{  \frac{ {x}^{2} - 4x - x + 4 -  {x}^{2}  - 3x - 2x + 6 }{(x - 2)(x - 4)}  =  \frac{10}{3} }} \\ \\

  \longrightarrow {\sf{  3({x}^{2} - 4x - x + 4 -  {x}^{2}  - 3x - 2x + 6 ) =  10(x - 2)(x - 4)}} \\ \\

  \longrightarrow {\sf{  3(2 {x}^{2} - 10x + 10 ) =  10( {x}^{2} - 4x - 2x + 8 )}} \\ \\

 \longrightarrow  {\sf{  6 {x}^{2} - 30x  + 30 =  10{x}^{2} - 40x - 20x + 8 0}} \\ \\

  \longrightarrow {\sf{   - 4 {x}^{2} + 30x   - 5 0 = 0}} \\ \\

  \longrightarrow {\sf{   4 {x}^{2}  -  30x    +  5 0 = 0}} \\ \\

  \longrightarrow {\sf{   2 {x}^{2}  -  15x    +  25 = 0}} \\ \\

  \longrightarrow{\sf{ x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ \\

  \longrightarrow{\sf{ x =  \frac{ 15 \pm \sqrt{ { (- 15)}^{2} - 4(2)(25) } }{2a} }} \\ \\

  \longrightarrow{\sf{ x =  \frac{  15 \pm \sqrt{ 225 - 200} }{4} }} \\ \\

  \longrightarrow{\sf{ x =  \frac{ 15 \pm \sqrt{ 25} }{4} }} \\ \\

  \longrightarrow{\sf{ x =  \frac{ 15 \pm 5}{4} }} \\ \\

  \longrightarrow{\sf{ x =  \frac{ 15  +  5}{4}, \frac{  15 - 5}{4}  }} \\ \\

  \longrightarrow{\sf{ x =  \frac{ 20}{4}, \frac{  10}{4}  }} \\ \\

  \longrightarrow{\sf{ x =  5, \frac{  5}{2}  }} \\ \\

\;\;\underline{\textbf{\textsf{Hence -}}}

\underline{\textsf{ Value of x is </p><p>\textbf{ 5 or, 5/2}}}.

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Answered by Anonymous
0

Answer:

Hey there

Step-by-step explanation:

5 is the answer

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