Question 37606
I can understand your frustration!
Let's see if I can help you...
Your LCD (x+2)(x+4) IS correct...
However, there is no need to FOIL it out here.
A simpler way to solve this type of equation is to cross multiply.
so...
(x-1)(x+4) = (x+2)(2x-3)
Then foil...
This way you skip two extra (unnecessary) steps!
x^2+3x-4 = 2x^2-x-6
Then, combine like terms...
Subtract x^2, 3x and -4 from both sides of the equation...
0 = x^2-4x-2
Then factor by using the quadratic equation...
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
For your equation a=1 b=-4 c=-2
So just substitute the variables...
Remember (-b) means OPPOSITE of the value of b.
So...
{{{x = (4 +- sqrt( -4^2-4*1*-2 ))/(2*1) }}}
Then simplify...
{{{x = (4 +- sqrt( 16+8 ))/(2) }}}
Then...
{{{x = (4 +- sqrt( 24 ))/(2) }}}
Simplify the square root of 24 as...
{{{x = (4 +- 2*sqrt( 6 ))/(2) }}}
Now factor the numerator then cancel...
{{{x = 2(2 +- 1)*sqrt( 6 )/(2) }}}
The 2's cancel...
{{{x = 2 +- sqrt( 6 )}}}
So the final answer is the solution set...
{{{x = 2 + sqrt( 6 )}}},{{{x = 2 - sqrt( 6 )}}}
I hope this helps!
Good Luck!
Let me know if you have any other questions!