Solve this Linear Equations::[tex] \frac{2x - 3}{2} - \frac{5}{x - 1} = x [/tex]Answer Should be -----[tex] - 1[/tex]Please No Rubbish, Answer it correctly, Answer Matching along with correct Process will get Brainlist.......​

Answers 1

Answer:

[tex]\displaystyle{\boxed{\red{\sf\:x\:=\:-\:\dfrac{7}{3}\:}}}[/tex]

Step-by-step-explanation:

The given equation is

[tex]\displaystyle{\sf\:\dfrac{2x\:-\:3}{2}\:-\:\dfrac{5}{x\:-\:1}\:=\:x}[/tex]

We have to find the value of x.

Now,

[tex]\displaystyle{\sf\:\dfrac{2x\:-\:3}{2}\:-\:\dfrac{5}{x\:-\:1}\:=\:x}[/tex]

[tex]\displaystyle{\implies\sf\:\dfrac{(\:2x\:-\:3\:)\:(\:x\:-\:1\:)\:-\:2\:\times\:5}{2\:(\:x\:-\:1\:)}\:=\:x}[/tex]

[tex]\displaystyle{\implies\sf\:\dfrac{2x\:(\:x\:-\:1\:)\:-\:3\:(\:x\:-\:1\:)\:-\:10}{2x\:-\:2}\:=\:x}[/tex]

[tex]\displaystyle{\implies\sf\:\dfrac{2x^2\:-\:2x\:-\:3x\:+\:3\:-\:10}{2x\:-\:2}\:=\:x}[/tex]

[tex]\displaystyle{\implies\sf\:2x^2\:-\:5x\:-\:7\:=\:x\:(\:2x\:-\:2\:)}[/tex]

[tex]\displaystyle{\implies\sf\:2x^2\:-\:5x\:-\:7\:=\:2x^2\:-\:2x}[/tex]

[tex]\displaystyle{\implies\sf\:2x^2\:-\:5x\:-\:2x^2\:+\:2x\:=\:7}[/tex]

[tex]\displaystyle{\implies\sf\:2x^2\:-\:2x^2\:-\:5x\:+\:2x\:=\:7}[/tex]

[tex]\displaystyle{\implies\sf\:-\:3x\:=\:7}[/tex]

[tex]\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:x\:=\:-\:\dfrac{7}{3}\:}}}}[/tex]

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