Solve for all values of x.

Question

x, plus, start fraction, 3, divided by, x, plus, 3, end fraction, equals, start fraction, 7, divided by, x, plus, 3, end fraction
x+
x+3
3
​
=
x+3
7
​

Answer 1

To solve this equation, cross multiply to eliminate the fractions:

(x + 3)(x + 3) = 3 * 7
(x^2 + 6x + 9) = 21
x^2 + 6x - 12 = 0

Now we have a quadratic equation. We can solve it by factoring:

(x + 3)(x - 2) = 0

Setting each factor to zero gives us:

x + 3 = 0 or x - 2 = 0
x = -3 x = 2

Therefore, the values of x are -3 and 2.

Answer 2

answer resalt in division by zero should be excluded

Answer 3

Apologies for the oversight. Let's exclude the value that makes the denominator become zero when solving for x:

x + 3 ≠ 0
x ≠ -3

Therefore, the only valid solution is x = 2.

Answer 4

are you sure

Answer 5

Let's re-evaluate the solution to ensure accuracy:

Given equation:

(x + 3)/(x + 3) = 7/(x + 3)

Since the left side of the equation simplifies to 1 for any value of x (unless x = -3, which is not included in the domain), we can simplify the equation to:

1 = 7/(x + 3)

Now, solving for x gives:

x + 3 = 7
x = 7 - 3
x = 4

Therefore, the only valid solution for x is x = 4.

Answer 6

Solve for all values of x.
x, minus, start fraction, 1, divided by, x, minus, 1, end fraction, equals, start fraction, 5, divided by, x, minus, 1, end fraction
x−
x−1
1
​
=
x−1
5
​

Answer 7

To solve this equation, we will cross multiply to eliminate the fractions:

x(x - 1) = 1 * 5
x^2 - x = 5
x^2 - x - 5 = 0

Now, let's solve this quadratic equation using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4*1*(-5))) / 2*1
x = (1 ± sqrt(1 + 20)) / 2
x = (1 ± sqrt(21)) / 2

Therefore, the solutions for x are:

x = (1 + sqrt(21)) / 2
x = (1 - sqrt(21)) / 2