solve. x/x-6 + 3 = 6/x-6?

Question

how do I go about doing this problem step by step. I am having no luck working this type of problem. thanks for your help.

Answer 1

Multiply both sides by x-6, if x ≠ 6
x + 3(x-6) = 6
=> 4x = 24
=> x = 6
Since x ≠ 6, there is no solution.

Answer 2

step one, move all X terms to the same side and all constants to the other.

3 = 6/x-6 - x/x-6

lucky for you the denominators are already the same, so subract your x tems

3 = 6-x/x-6

know that 3 is the same as 3/1 and cross multiply

3/1 = 6-x/x-6

3(x-6) = (6-x)

distribute

3x - 18 = 6 - x

group like terms

3x + x = 6 + 18

4x = 24

divide through by 4

x = 6

that is how you would do that TYPE of problem, but check to make sure you entered it correctly because x should not be = to 6, because that would make 6/ (6-6) in the original question, which is 6/0 which is undefined

Answer 3

Please placed parentheses around the completed denominator. it somewhat is complicated to tell in case you advise: 3/x + 6 or 3/(x + 6) x/x + 2 or x/(x + 2) Do you notice the version? in case you do not care to make the attempt to try this, why could we care to make the attempt that may well be useful you? additionally, interior the solutions, please placed parentheses around the completed numerator and denominator. i'm assuming you advise: 3/(x + 6) + x/(x + 2) subsequently, we want them to have a basic denominator to function the fractions. We multiply the coolest and backside of the left fraction with the help of (x + 6). Then we multiply the coolest and backside of the splendid fraction with the help of (x + 2). this provides us: [ 3*(x + 2) ] / [ (x + 6)(x + 2) ] + [ x(x+6) ] / [ (x + 6)(x + 2) ] Now that the denominators are a similar, we are in a position to upload the numerators to get: [ 3*(x + 2) + x(x+6) ] / [ (x + 6)(x + 2) ] we could amplify the words interior the numerator. [ 3*x + 3*2 + x*x + x*6 ] / [ (x + 6)(x + 2) ] Simplify [ 3x + 6 + x² + 6x ] / [ (x + 6)(x + 2) ] [ x² + 9x + 6 ] / [ (x + 6)(x + 2) ] that feels like answer A, yet if you consider which you probably did not placed the parentheses around the completed numerator, it somewhat is complicated to tell. i've got considered you ask numerous of a similar style of questions. attempt appearing a number of those your self, i've got written out the stairs for you and am attempting to coach you!

Answer 4

The easiest solution is to multiply the entire problem by 'x - 6'.

(x-6)*(x/x-6) + (x-6)*3 = (x-6)*(6/x-6)
x + 3x - 18 = 6
x + 3x = 24
4x = 24
x = 6

However, 6 does not work here: if you plug it back into the original problem, then you end up with 0 in the denominator. There are no real solutions to this problem.

Answer 5

I am going to assume you actually meant

x/(x-6) + 3 = 6/(x-6)

Multiply both sides by (x-6):

x + 3(x - 6) = 6

Distribute:

x + 3 x - 18 = 6

Combine like terms:

4 x - 18 = 6

Add 18 to each side:

4x = 24

Divide each side by 4:

x = 6.

But since replacing x with 6 in the original equation results in division by zero, there i no solution.

Answer 6

The first thing you need to know about this problem is that x≠6.

Multiply both sides by x-6:
x+3(x-6)=6
x+3x-18=6
4x-18=6
4x=24
x=6
No solution because you cannot divide a number by zero.

Check:
6/6-6+3=6/6-6
6/0+3=6/0
That is false!

Answer 7

so you start with x/(x-6) + 3 = 6 / (x-6) now, multiply both sides by (x-6) so you get

(x *(x-6))/(x-6) + 3(x-6) = 6 looking at the first part, the x*(x-6)/(x-6) cancels out to just a simple x

now you have : x + 3x -18 = 6 and simplify

4x = 24
x = 6

since (6) - 6 = 0 there is no solution

Answer 8

1. multiply the whole equation by (x-6) to get rid off the fractions
you get: x + 3(x-6) = 6
2. then simply solve the equation without fractions
x+ 3x -18 = 6
4x = 24
x=6
3. if x= 6 that you would have the denominator equal to zero (6-6= 0), so this equation has no solution

Answer 9

x÷x-6+3=6÷x-6
-3 -3
0 -9
x÷x-6 =6÷x-9
+6 +6
0 -3
x÷x =6÷x-3
x÷x =6-3÷x
x÷x =3÷x
x =3÷x
im not sure if its right but hope i helped

Answer 10

first multiply everything by x-6.
1) x+3(x-6)=6
2) distribute x+3x-18=6
3)simplify 4x=24
4)solve x=6

6 is not possible so no solution