Question

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Answer 1

1)\(\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\)

⇔\(\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\)

⇔\(4x-5=2\left(x-1\right)+x\)

⇔\(4x-5=2x-2+x\)

⇔\(4x-5-2x+2-x=0\)

⇔\(x-3=0\)

⇔\(x=3\)

2)\(\dfrac{7}{x+2}=\dfrac{3}{x-5}\)

⇔\(7\left(x-5\right)=3\left(x+2\right)\)

⇔\(7x-35=3x+6\)

⇔\(7x-35-3x-6=0\)

⇔\(4x-41=0\)

⇔\(4x=41\)

⇔\(x=\dfrac{41}{4}\)