problems on solving rational equation

**lickman** · October 25th 2008, 10:24 AM

so i've been given a question :
5x / x-4 = 3x/2x + 7

and i had to solve for x, or the root u can say. I've gotten to the step where i cross multiply and bring everything to one side. And i got
7x^2 + 42 x, i'm not sure from here on how to solve for x or the roots.

i also have another rational problem like this :
x / x -2 = x^2-4x + 1/ x-3
and i have gotten to the step of bring everything to one side :
x^3 - 7x^2 + 12x -2 i'm not sure is this correct. but my teacher told me to solve with polynomial divison but i cannot find anything sets that polynomial to 0. so please help :S

**vincisonfire** · October 25th 2008, 10:32 AM

$\frac{5x}{x-4} = \frac{3x}{2x + 7}$
$5x \dot (2x+7) = 3x \cdot (x-4)$
$10x^2 + 35x = 3x^2 - 12x$
$7x^2 + 47x = 0$
Divide everything by x
$7x + 47 = 0$
$x = -\frac{47}{7}$

**vincisonfire** · October 25th 2008, 10:46 AM

$\frac{x}{x -2} = \frac{x^2-4x + 1}{x-3}$
$(x) \cdot (x-3) = (x^2-4x+1) \cdot (x-2)$
$x^2 - 3x = x^3 - 4x^2+x-2x^2+8x-2$
$0 = x^3 - 7x^2+12x-2$
This has no rational roots.
Let $x = z - \frac{a}{3}$
Equation take form $0 = z^3 + pz + q$
That you can solve with a long messy method Cubic function - Wikipedia, the free encyclopedia
Sorry there is not always a simple way.

Math Help - problems on solving rational equation

LinkBack

Thread Tools

Display

problems on solving rational equation

Similar Math Help Forum Discussions

solving rational equation

Problems solving an equation with sum

Solving Problems with Rational Expressions

Solving Rational Equation's Oblique(slant) Asymptote

Please Help.Solving Rational Equation

Search Tags