I need some help

[HBoom]

Hello all,

So, I am learning math at the moment, and all is going great. But now I am trying to solve a question, and I have tried it for hours already but no succes:

\(\displaystyle \dfrac{2}{2x - 3} + \dfrac{3}{x + 5} = 6\)

I made the graph on my calculator and calculated the intersections, and came to the conclusion that \(\displaystyle x \approx -4.51\) and \(\displaystyle x \approx 1.68\).
But I have no idea how to solve this manually.

Could anyone please push me in the right direction?

Thank you so much.

 

[willmoore21]

Can you multiply through by one of the denominators? Do you know how to do this?

If you can, do this, and simplify, then move everything over to one side and you should notice something about what you have left.

Show your workings and don't hesitate to reply if you get stuck again.

 

[HBoom]

Can you multiply through by one of the denominators? Do you know how to do this?

If you can, do this, and simplify, then move everything over to one side and you should notice something about what you have left.

Show your workings and don't hesitate to reply if you get stuck again.

Ah I finally got it!

\(\displaystyle (\dfrac{2}{2x-3})(\dfrac{x+5}{x+5}) + (\dfrac{3}{x+5})(\dfrac{2x-3}{2x-3}) = (\dfrac{6}{1})(\dfrac{2x^2+7x-15}{2x^2+7x-15})\)


\(\displaystyle
8x+1 = 12x^2+42x-90
\)


\(\displaystyle
12x^2+34x-91 = 0
\)


\(\displaystyle
D = 34^2-4*12*-91 = 5524
\)


\(\displaystyle
x_1 = \dfrac{-34+\sqrt{5524}}{2*12} \approx 1,68
\)


\(\displaystyle
x_2 = \dfrac{-34-\sqrt{5524}}{2*12} \approx -4,51
\)

 

[willmoore21]

Glad it helped.