Question

Please help me, ive tried and cant get it right

Answer 1

Given:

an equation is given as

`(1)/(x)+(1)/(x-10)=(x-9)/(x-10)`

Find:

we have to solve the given equation.

Step-by-step explanation:

We will solve the equation by taking LCM as following

`\begin{gathered} (1)/(x)+(1)/(x-10)=(x-9)/(x-10) \\ (x-10+x)/(x(x-10))=(x-9)/(x-10) \\ (2x-10)/(x-10)=(x(x-9))/(x-10) \\ 2x-10=x^2-9x \\ x^2-9x-2x+10=0 \\ x^2-11x+10=0 \\ x^2-10x-x+10=0 \\ x(x-10)-1(x-10)=0 \\ (x-10)(x-1)=0 \\ x=1,10 \end{gathered}`

But the given equation is undefined for x = 10,

Therefore, x = 1 is the only solution of the given equation.