Please Help.Solving Rational Equation

**whoa** · November 8th 2006, 01:23 AM

Please help me with this equations:

1.) 13/x^2-9x+14 = 5/x-3 + 3x-7/x^2+2x-15

2.) 3x/x+1 - 1/3 = 5/x+1

3.) 11/x+5 - 5/x-3 = 3x-7/x^2+2x-15

4.) 17/y + 13/y+2 = 14/y^2-12y

5.) y/y-8 - 48/y^2-64 = y/y+8

thank you for your kind consideraton :-)

**CaptainBlack** · November 8th 2006, 03:21 AM

Originally Posted by whoa

Please help me with this equations:

1.) 13/x^2-9x+14 = 5/x-3 + 3x-7/x^2+2x-15

2.) 3x/x+1 - 1/3 = 5/x+1

3.) 11/x+5 - 5/x-3 = 3x-7/x^2+2x-15

4.) 17/y + 13/y+2 = 14/y^2-12y

5.) y/y-8 - 48/y^2-64 = y/y+8

thank you for your kind consideraton :-)

Please add brackets to make the meaning of these expressions clear
and unambiguous. Otherwise the helpers are going to have to guess
what you mean and may waste their time answering the wrong questions

RonL

**Soroban** · November 8th 2006, 04:34 AM

Hello, whoa!

Is there a typo in #1?
We end up with an ugly cubic equation.

I'll do #2 . . .

$2)\;\frac{3x}{x+1} - \frac{1}{3} \:= \:\frac{5}{x+1}$

Find the LCD and multiply through by it . . .

The LCD is: $3(x+1)$

We have: . $3(x+1)\cdot\frac{3x}{x+1} -\, 3(x+1)\cdot\frac{1}{3} \;= \;3(x+1)\cdot\frac{5}{x+1}$

Cancel and get: . $3\cdot3x - (x + 1) \;=\;3\cdot5$

. . .Solve for $x\!:$ . . . . $9x - x - 1 \;=\;15$

. . . . . . . . . . . . . . . . . . . . $8x \;= \;16$

. . . . . . . . . . . . . . . . . . . . . $\boxed{x\;=\;2}$

**earboth** · November 8th 2006, 05:17 AM

Originally Posted by whoa

Please help me with this equations:...
3.) 11/x+5 - 5/x-3 = 3x-7/x^2+2x-15
...
thank you for your kind consideraton :-)

Hello, whoa,

1. The LCD is $(x+5)(x-3) = x^2 +2x-15$

2. Multiply by LCD:

$11(x-3)-5(x+5) = 3x-7$

3. Multiply the brackets and rearrange:

$11x-33-5x-25=3x-7\ \Longleftrightarrow \ 3x=51$

So x = 17

**earboth** · November 8th 2006, 05:30 AM

Originally Posted by whoa

Please help me with this equations:...
5.) y/y-8 - 48/y^2-64 = y/y+8
thank you for your kind consideraton :-)

Hello, whoa,

1. The LCD is: $(y+8)(y-8)=y^2-64$

2. Multiply by LCD

$y(y+8)-48=y(y-8)$ . Multiply the brackets and rearrange:

$y^2+8y-48=y^2-8y\ \Longleftrightarrow\ 3y=48$

Thus y = 3

EB

**Soroban** · November 8th 2006, 06:55 AM

Hello, whoa!

$1)\;\;\frac{13}{x^2-9x+14} \:= \:\frac{5}{x-3} + \frac{3x-7}{x^2+2x-15}$

We have: . $\frac{13}{(x-2)(x-7)} \;=\;\frac{5}{x-3} + \frac{3x-7}{(x-3)(x+5)}$

The LCD is: $(x-2)(x-3)(x-7)(x+5)$

Multiply through by the LCD:

. . $13(x-3)(x+5) \:=\:5(x-2)(x-7)(x+5) + (3x-7)(x-2)(x-7)$

which simplifies to that ugly cubic I promised you:

. . $8x^3 - 80x^2 + 94x + 447 \;= \;0$ . . . ack!

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I conclude that you copied the first fraction incorrectly.

Problem #1 is expected to be simple and straight-forward.
. . I suspect that its denominator is $x + 5$ .

Can you please get back to us?

**whoa** · November 8th 2006, 12:40 PM

Thank you guys!

oh by the way, i'd copied number 1 right, I think my math instructor made a mistake.

thanks again for your answers!

Thread: Please Help.Solving Rational Equation

LinkBack

Thread Tools

Display

Please Help.Solving Rational Equation

nr. 3 only

nr. 5 this time

Similar Math Help Forum Discussions

solving rational equation

Rational equation, rational expression, simplifying,

Solving Rational Equation's Oblique(slant) Asymptote

solving rational equations

problems on solving rational equation

Search Tags