Question

raízes da equação 1/2 = 3/2 - 1/x-1

Answer 1

Dada a equação:

$\mathsf{\dfrac{1}{2}=\dfrac{3}{2}-\dfrac{1}{x-1}}$

Resolvendo:

$\mathsf{\dfrac{1}{\diagup\!\!\!\!2}=\dfrac{3\left(x-1\right)-\left(1\cdot 2\right)}{\diagup\!\!\!\!2\cdot \left(x-1\right)}}\\\\\\\mathsf{1=\dfrac{3\left(x-1\right)-\left(1\cdot 2\right)}{x-1}}\\\\\\\mathsf{x-1=3\left(x-1\right)-2}\\\\\\\mathsf{x-1=3x-3-2}\\\\\\\mathsf{x-1=3x-5}\\\\\\\mathsf{3x-x=5-1}\\\\\\\mathsf{2x=4}\\\\\\\mathsf{x=\dfrac{4}{2}}\\\\\\\mathsf{x=2}$

= = = = =

Por se tratar de uma equação polinomial do 1ª grau, possui apenas uma raiz real:

$\boxed{\mathsf{S=\left\{x\in \mathbb{R}\:,\:x=2\right\}}}\: \: \checkmark$