Solve using LCD.?

Question

I need both of these solved i can't do them on my own thanks.

5/x + 3 + x/4 = -3


x/2x + 10 = x - 9/x - 7

Answer 1

1.5/x+3+x/4=-3.
multiply both sides by LCD=4(x+3)
20+x(x+3)=-3*4(x+3)
20+x^2+3x=-12x-36
x^2+15x+56=0
(x+8)(x+7)=0
x=-7,-8. ANS
2. x/2x. it appears there is mistake in digiting

Answer 2

5/x + 3 + x/4 = -3.
Assuming that x is not 0, multiply by 4x
4x(5/x) + 4x(3) + 4x(x/4) = 4x(-3)
20 + 12x + x^2 = -12x
x^2 +24x + 20 = 0
x^2 + 24x + 144 = -20 + 144 = 124
(x + 12) = +/- sqrt(124) = +/- 2sqrt(31)
x = -12 +/- 2sqrt(31)

same for the second:
clear the fractions by multiplying both sides by 2x. Simplify and solve the quadratic. If 0 comes up as a solution, you must discard it since it is not a solution to the original problem.

Answer 3

5/x + 3 + x/4 = -3
5/(x+3) + x/4 = -3 <--- Assume you meant this
4*5(x+3) + x(x+3) = -3*4(x+3) [LCD = 4(x+3)]
20x +60 +x^2 +3x = 12x+36
x^2 +11x + 24 = 0
(x+8)(x+3)=0
x = -8 or -3

x/2x + 10 = x - 9/x - 7
x/(2x+10) = (x-9)/(x-7) <-- Assume you meant this
Now just cross multiply and solve.

Answer 4

5/x + 3 + x/4 = -3
Multiply with x to each:
5 + 3x + x^2 = -3x
x^2 + 3x + 5 + 3x = 0
x^2 + 6x + 5 = 0
In order to result 5, the only possibilities is x * x.
In order to result 5, the only possibilities is 1 * 5.
Hence, you can only use combination x * x and 1 * 5.
x^2 + 6x + 5 = 0
(x+1)(x+5) = 0
x + 1 = 0
x = -1
or
x + 5 = 0
x = -5

x/2x + 10 = x - 9/x - 7
Mutiply each with 2x:
x + 20x = 2x^2 - 18 - 14x
0 = 2x^2 - 18 - 14x - x -20x
0 = 2x^2 - 35x - 18

In order to result 2x^2, you can only use 2x * x.
In order to result -18, you can use -1 * 18, -18 * 1, -2 * 9, -9 * 2, -3 * 6, -6 * 3.
In order to result -35x, you can have this: 2x * (-18) + x * 1.
Hence, the combination you have to use is :
2x * x and -18 * 1 .
0 = 2x^2 - 35x - 18
0 = (2x +1)(x-18)
2x + 1 = 0
2x = -1
x = -1/2
or
x-18 = 0
x = 18

Answer 5

1. 5/x + 3 + x/4 = -3
5/x +x/4 = -6
pretend like you're trying to get a common denominator on any normal problem without variables. cross-multiply to get the tops, and multiply the denominators together to get the common denom. or just multiply 5/x by 4/4 and x/4 by x/x. also, don't forget to multiply the -6 by 4x/4x
20/4x + x^2/4x= -24x/4x
20/4x + x^2/4x= -6x
mult. by 4x
20 + x^2= -24x^2
20=-25x^2
hmmm....seems weird. you may have to quadratic that, but I prolly messed it up, so as not to confuse you further, I'm stopping here. sorry. maybe you'll catch my mistake if someone else doesn't answer it.

Answer 6

5/x + 3 + x/4 = - 3
20/4x + 12x/4x + x^2/4x = - 3
(20 + 12x + x^2) / 4x = - 3
20 + 12x + x^2 = - 12x
20 + x^2 = - 12x - 12x
20 + x^2 = - 24x
x^2 + 24x = - 20
x = - 0.864472

Answer: x = - 0.864472