Subject:
MathAuthor:
clementineCreated:
1 year agoAnswer:
[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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