Thread: Algebraic Fractions: Is this method correct?

It would really help if you wrote the fractions in a non-ambiguous way... did you mean ? or ? or something else? It is very hard to understand...

If you meant the first, then:

Now solve for x and that is your solution (use the quadratics formula )

Thank you for replying, (you read the equation correctly) but your response is a little unclear beyond the middle section.


Cross multiplying to obtain (x+5)(2x-3) = 8x makes perfect sense, as does expanding the brackets on the left side. However I can't follow how 8x translates to 16x - 24

I appears as if the 8x value is discarded, and 8 is re multiplied against 2x-3

Would this be what it is supposed to look like:



and could you clarify this?

Thanks

Cross multiplying gives you:



Expanding the LHS and collecting like terms



Use the quadratic formula to find the solutions.

Which are or

Originally Posted by vbiter

I am having trouble finding the correct method for solving algebraic fractions. I have tried the sequence of operations below and it appears to fit, but would appreciate some help / guidance on a robust process for working through to solve these equations. Thanks





can be rewritten as

which cancels out to

No, it doesn't. If you mean (x+5)/x, that is equal to 1+ 5/x, not 5.

Assuming that you mean (x+5)/x= 8/(2x-3), I would recommend that you get rid of the fractions by multiplying both sides by the denominators x(2x-3)

Multiplying the left side by x(2x-3) cancels the "x"s and gives (x+5)(2x-3). Multiplying the right side by x(2x-3) cancels the "2x-3"s and gives 8(x). So your equation becomes (x+5)(2x-3)= 8x. That is a quadratic equation for x.

which can be rewritten as

and therefore

and

==>

Originally Posted by vbiter

Thank you for replying, (you read the equation correctly) but your response is a little unclear beyond the middle section.


Cross multiplying to obtain (x+5)(2x-3) = 8x makes perfect sense, as does expanding the brackets on the left side. However I can't follow how 8x translates to 16x - 24

I appears as if the 8x value is discarded, and 8 is re multiplied against 2x-3

Would this be what it is supposed to look like:



and could you clarify this?

Thanks

Oops, don't know what happened there... fixed the original post now.