How do I solve these equations?

Question

1/4 - 6/x = 3/x

x+2/2 = 4/x

6/x+4 + 3/4 = 2x+1/3x+12

Answer 1

1/4 - 6/x = 3/x

Multiply by x

x/4 - 6 = 3

Add 6

x/4 = 9

Multiply by 4

x = 36


Q2)

(x+2)/2 = 4/x

Cross Multiply

x^2 + 2x = 8

x^2 + 2x - 8 = 0

Factor

(x + 4)(x - 2) = 0

x + 4 = 0
x = -4

x - 2 = 0
x = 2

Q3)

6/(x+4) + 3/4 = (2x+1)/(3x+12)

Multiply by 3x + 12

6(3) + 3(3x + 12)/4 = 2x + 1

18 + 9/4x + 9 = 2x + 1

9/4x + 27 = 2x + 1

1/4x = -26

x = -104

Answer 2

First, use parentheses where needed for clarity, then multiply through by LCD.

1/4 - 6/x = 3/x
x - 24 = 12
x = 36

(x+2)/2 = 4/x
2x(x+2)/2 = 4*2x/x
x^2 + 2x = 8
x^2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = - 4, 2

6/(x + 4) + 3/4 = (2x + 1)/(3x + 12)
24(3x + 12) + 3(x + 4)(3x + 12) = 4(x + 4)(2x + 1)
72x + 288 + 3(3x^2 + 24x + 48) = 4(2x^2 + 9x + 4)
72x + 288 + 9x^2 + 72x + 144 = 8x^2 + 36x + 16
x^2 + 108x = - 416
x^2 + 72x + 54^2 = 2,916 - 416
(x + 36)^2 = 2,500
x + 36 = ± 50
x = -86, 14

Answer 3

i think u need to use parantheses so we understand better,

for the second one u cross multiply
x(x+2) = 4(2)
that would be (x^2)+2x=8
and then you would go (x^2)+2x-8=0
and then you factor and get (x+4)(x-2) so the answer is
x = -4 or 2



the 1st one u change it to
(1/4) = (3/x)+(6/x) and u can add across and get
9/x=(1/4)
x= 9/(1/4)


for the 3rd i'm not sure cuz no parentheses
but this is wat i got:
make common denominators it's too long
((-2(x^2)) + 27x + 4) / ((3(x^2)) + 12)

Answer 4

1/4-6/x=3/x
4x^2 is lcd

x^2-24x-12x=12x-12x
x^2-36x=0
x(x-36)=0
x=0 x=36

x+2/2=4/x
use 2x as lcd
x(x+2)=8
x^2+2x-8=0
(x+4)(x-2)=0
x=-4 x=2

6/x+4 +3/4=2x+1/3x+12

3x+12 is lcd

18+3(x+12=2x+1
18+3x+36=2x+1
54+3x=2x+1
x=-53

Answer 5

this might look complicated, even however that's certainly fairly trouble-free. i'm going to do huge variety 2 for you because of the fact this is the toughest. 2(6x+3)=3(2x+12) one million. you may desire to distribute the two and the three. this provide you: 12x+6=6x+36 2. Now you may desire to get "x" to a minimum of one ingredient of the equation and the each and every thing else to the different. Subtract 6x from the two facets. You get: 6x+6=36 as quickly because it fairly is finished, you may desire to subtract the "6" from the two facets. 6x=36 3. Now you may desire to unravel for "x" by dividing the two facets by 6. this provide you "x'' on one ingredient. 36 divided by 6 = 6 the respond is x=6 question one million is x=-3 question 2 is x=6 question 3 is x=-3 desire that made experience !

Answer 6

u used a calculator!!! lol

Answer 7

you ask SmarterChild.