If 1/x - 1/x+3 = 1/x+2 - 1/x-5 then the 2 solutions for x are -3+2(square root of)k/w. Find the value of k+w.
2007-01-16 12:11:59 · 6 answers · asked by SallyJane 3 in Science & Mathematics ➔ Mathematics
Think about the quadratic formula. Hold that thought. Now look at the equations and simplify:
1/x - 1/(x+3) = (x+3)/x(x+3) - x/x(x+3) = (x+3-x)/x(x+3)
1/(x+2) - 1/(x-5) = [(x-5) - (x+2)]/(x+2)(x-5) = -7/(x+2)(x-5)
These two are equal:
3/x(x+3) = -7/(x+2)(x-5)
-7x(x+3) = 3(x+2)(x-5)
-7x^2 -21x = 3(x^2-3x-10) = 3x^2 - 9x - 30
Now combine like terms and get into the form of quadratic eqn:
10x^2 +12x - 30 = 0 or dividing both sides by 2
5x^2 + 6x - 15 = 0
Now put into the quadratic equation:
x = {-6 +- sqr[36 - 4(5)(-15)]}/2(5)
= {-6 +- sqr[36 + 300]}/10
now the sqr[336] = 4sqr[21], so now you have
x = {-6 +- 4sqr[21]}/10 = {-3 +- 2sqr[21]}/5
so k = 21 and w = 5
2007-01-16 12:30:17 · answer #1 · answered by kellenraid 6 · 0⤊ 0⤋
you must get common denominators on both sides in order to add the numerators on each side. after you do this u get this:
3/x(x+3)=-7(x+2)(x-5)... u now have a proportion. cross multiply:
3x^2-9x-30=-7x^2-21x....now move all terms to the left so that the equation is equal to zero. u have a quadratic equation. use quad. formula.
10x^2+12x-30=0
-12+ or -sqrt1344/20 then....-12+or-8sqrt21/20...then divide three outside numbers, -12, 8 &20 by 4 and get...
-3+or-2sqrt21/5 so your k and w are 21 AND 5.
2007-01-16 20:38:29 · answer #2 · answered by robert s 5 · 0⤊ 0⤋
The answer is blue minus 1/2
2007-01-16 20:16:00 · answer #3 · answered by ttpawpaw 7 · 0⤊ 1⤋
hmm, all i kno is that 2+2= 5
2007-01-16 20:15:43 · answer #4 · answered by jared B 2 · 0⤊ 1⤋
yea like we know that
2007-01-16 20:15:06 · answer #5 · answered by Shawn M 1 · 0⤊ 1⤋
wow... can you explain that to me in English please? haa haa
2007-01-16 20:14:12 · answer #6 · answered by wind it up 4 · 0⤊ 1⤋