Question

Consider this rational equation.二+-==Use the least common denominator to simplify the rational equation into a standard form quadratic equation.Replace the values of b and to create the equation.

Answer 1

`\begin{equation*} x^2-10x+8=0 \end{equation*}`

Step-by-step explanation

We want to rewrite the rational equation as a quadratic equation:

`(1)/(x)+(1)/(x-2)=(1)/(4)`

First, let us find the lowest common denominator for the left-hand side of the equation:

`\begin{gathered} (1)/(x)+(1)/(x-2)=(1)/(4) \\ \\ (x-2+x)/(x(x-2))=(1)/(4) \\ \\ (2x-2)/(x^2-2x)=(1)/(4) \end{gathered}`

Next, cross-multiply:

`\begin{gathered} 4(2x-2)=x^2-2x \\ \\ 8x-8=x^2-2x \end{gathered}`

Finally, move all the terms to the left-hand side and simplify:

`\begin{gathered} 8x-8-x^2+2x=0 \\ \\ -x^2+2x+8x-8=0 \\ \\ -x^2+10x-8=0 \\ \\ \Rightarrow x^2-10x+8=0 \end{gathered}`

That is the answer.