1. ## solving rational equations

x-1 + x-3 = x+13
x+5 x+2

If someone could do this step by step would help me a ton and would be appreciated.

I am confused about the LCD is it LCD=(x+5),(x+2)?
because when I do on the right side of the = it is (x+13)(x+5)(x+2) and I think thats wrong because she said in our class we wont foil three sets of brackets.

2. Originally Posted by brentwoodbc
x-1 + x-3 = x+13
x+5 x+2

If someone could do this step by step would help me a ton and would be appreciated.

I am confused about the LCD is it LCD=(x+5),(x+2)?
because when I do on the right side of the = it is (x+13)(x+5)(x+2) and I think thats wrong because she said in our class we wont foil three sets of brackets.
FOIL the last 2 sets first, you get

$\displaystyle (x+13)(x^2 + 7x + 10)$

Then multiply everything in the first bracket by everything in the second, so it becomes

$\displaystyle x(x^2 + 7x + 10) + 13(x^2 + 7x + 10)$.

3. Originally Posted by Prove It
FOIL the last 2 sets first, you get

$\displaystyle (x+13)(x^2 + 7x + 10)$

Then multiply everything in the first bracket by everything in the second, so it becomes

$\displaystyle x(x^2 + 7x + 10) + 13(x^2 + 7x + 10)$.
-7, 11 +/-sqrt37
2

just need to figure that out thanks agian though.

4. Originally Posted by Prove It
FOIL the last 2 sets first, you get

$\displaystyle (x+13)(x^2 + 7x + 10)$

Then multiply everything in the first bracket by everything in the second, so it becomes

$\displaystyle x(x^2 + 7x + 10) + 13(x^2 + 7x + 10)$.
-7, 11 +/-sqrt37
--------2

just need to figure that out thanks agian though. because u get an x^3 term and you need to factor it .

5. Originally Posted by brentwoodbc
-7, 11 +/-sqrt37
--------2

just need to figure that out thanks agian though. because u get an x^3 term and you need to factor it .
Once you've expanded everything and equated it to 0, you should get a linear factor and a quadratic factor.

Then you solve the linear factor using the null factor law and the quadratic factor using the null factor law and quadratic formula.

the LCD is (x+5)(x+2)

if you mulitply ech term by the LCD you will eliminate the fractions and have (x-1)(x+2)+(x-3)(x+5)=(x+13)(x+5)(x+2)

FOIL the 1st and 2nd terms and mulitply the last terms and you now have:
x^2+2x-x-2+x^2+5x-3x-15+x^3+7x^2+10x+13x^2+91x+130

Combine like terms on each side and you have:
2x^2+3x-17=x^3+20x^2+101x+130

Get all terms to the left side and you now have:
-x^3-18x^2-98x-147=0

from here use synthetic division or factor by grouping...hope this helped!