Question

Solve the rational equation.
3/x+1/x - 5=1/2x

Answer 1

\[\Large \frac3x+\frac1x-5=\frac12x\] do you mean this??

Answer 2

\[\Large \frac{3+1}{x}-\frac{5x}{x}=\frac x2 \Longrightarrow \frac{4-5x}{x}=\frac x2\]

Answer 3

then use cross multiplication ....

Answer 4

\[\Large 2\cdot(4-5x)=x^2 \Longrightarrow 8-10x=x^2\]

\[\Large \boxed{ x^2+10x-8=0 }\]

Answer 5

Now use quadratic formula... \[\LARGE x_{1/2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 6

can you continue or would you like me to finish it ?? :D

Answer 7

@rosa15baez do you understand it ?

Answer 8

yea could you finish it

Answer 9

with pleasure ..

Answer 10

substitute ...\[\Large x_{1/2}\frac{-10\pm\sqrt{10^2-4\cdot 1\cdot (-8)}}{2\cdot 1}\] multiply/simplify ...\[\Large x_{1/2}\frac{-10\pm \sqrt{132}}{2} \] from here you get...\[\Large x_1=\frac{-10 + \sqrt{132}}{2} \quad ,\quad x_2=\frac{-10 - \sqrt{132}}{2}\]

Answer 11

that's it... if you want to calculate it , use calculator, It seems they're not integers