rational equations: what do solutions represent on graph?

[dayton1]

OK one more-

I solved a rational equation and got X=5/14.......I was asked what the solution represents on a graph....I said it represented where the graph of the equation crosses the x-axis.....am I way off :?

 

[Deleted member 4993]

To answer that - we need to know what that "rational equation" was.

What was it - can you please tell us?

 

[dayton1]

sorry :lol: Ok lets see if I can write this out:

2x+1/x^2-3x-10 + x-1/x^2-4 = 3x-1/x^2-7x+10

 

[stapel]

2x+1/x^2-3x-10 + x-1/x^2-4 = 3x-1/x^2-7x+10

The above means the following:

. . . . .2x + (1/x²) - 3x - 10 + x - (1/x²) - 4 = 3x - (1/x²) - 7x + 10

Is that what you meant? Or is the equation more along the lines of the following?

. . . . .(2x + 1)/(x² - 3x - 10) + (x - 1)/(x² - 4) = (3x - 1)/(x² - 7x + 10)

Thank you!

Eliz.

 

[Deleted member 4993]

sorry :lol: Ok lets see if I can write this out:

2x+1/x^2-3x-10 + x-1/x^2-4 = 3x-1/x^2-7x+10

First - you cannot graph an equation.

You can graph a function. In your case that function would be

\(\displaystyle f(x) = \frac{2x+1}{x^2-3x-10} + \frac{x-1}{x^2-4} - \frac{3x-1}{x^2-7x+10}\)

your solution represents the value of 'x' where f(x) = 0

 

[dayton1]

The bottom one that you wrote is right Eliz

 

[dayton1]

What does the solution mean. To check the solution I can just plug x back into the equation right?