Question

6/(x^2-3x)=12/x+1/(x-3) with full expanation from the internet

Answer 1

`x=(42)/(13)`

Explanation:

Given equation:

`(6)/((x^2-3x))=(12)/(x)+(1)/((x-3))`

Factor the denominator on the left side:

`\implies (6)/(x(x-3))=(12)/(x)+(1)/((x-3))`

Combine the fractions on the right side by multiplying by the LCM:

`\begin{aligned}\implies (6)/(x(x-3)) & =(12)/(x) \cdot ((x-3))/((x-3))+(1)/((x-3)) \cdot (x)/(x)\\\\& =(12(x-3))/(x(x-3))+(x)/(x(x-3))\\\\& =(12(x-3)+x)/(x(x-3)) \end{aligned}`

As the denominators are now the same on both sides:

`\begin{aligned}\implies (6)/(x(x-3)) & =(12(x-3)+x)/(x(x-3))\\\\ \implies 6 & = 12(x-3)+x\end{aligned}`

Simplify and solve for x:

`\begin{aligned}\implies 6 & = 12(x-3)+x\\\\6 & =12x-36+x\\\\6 & =13x-36\\\\13x & =42\\\\\implies x & =(42)/(13)\end{aligned}`