√x+3/ x+3 = 1
what is the solve for x?
To solve the equation √x + 3 / (x + 3) = 1, we can start by isolating the square root term on one side.
First, we want to get rid of the fraction. Multiply both sides of the equation by (x + 3):
[(x + 3) * √x + 3] / (x + 3) = 1 * (x + 3)
This simplifies to:
√x + 3 = x + 3
Now, subtract 3 from both sides of the equation:
√x = x
To solve for x, we need to eliminate the square root. Square both sides of the equation:
(√x)^2 = x^2
This simplifies to:
x = x^2
Rearrange the equation:
x^2 - x = 0
Now, factor out x to solve:
x(x - 1) = 0
This equation is satisfied when either x = 0 or x - 1 = 0. Thus, the solutions for x are x = 0 and x = 1.
what is the solve for that?
Apologies for the confusion. Let's solve for x again step by step:
√x + 3 / (x + 3) = 1
To get rid of the fraction, multiply both sides by (x + 3):
√x + 3 = 1 * (x + 3)
√x + 3 = x + 3
Now, subtract 3 from both sides:
√x = x
Square both sides to eliminate the square root:
(√x)^2 = x^2
x = x^2
Rearrange the equation:
x^2 - x = 0
Factor out x:
x(x - 1) = 0
This equation is satisfied when either x = 0 or x - 1 = 0.
If x = 0, the equation holds true.
If x - 1 = 0, solving for x gives x = 1.
Therefore, the solutions for x are x = 0 and x = 1.
- 2 1/3 - (-5)= ?
To simplify the expression -2 1/3 - (-5), let's convert the mixed number -2 1/3 to an improper fraction first.
-2 1/3 is the same as -2 + 1/3.
To convert 2 to an improper fraction, we multiply the whole number (-2) by the denominator of the fraction and add the numerator:
2 * 3 + 1 = 6 + 1 = 7.
Now, we have -2 1/3 as -7/3.
-7/3 - (-5) = -7/3 + 5.
In order to add these fractions, we need to find a common denominator. The common denominator is 3:
(-7/3) + (5 * 3/3) = -7/3 + 15/3.
Now that we have the same denominator, we can combine the numerators:
-7/3 + 15/3 = 8/3.
Therefore, -2 1/3 - (-5) simplifies to 8/3.
To solve for x in the equation √(x+3)/(x+3) = 1, we can follow these steps:
Step 1: Multiply both sides of the equation by (x+3) to eliminate the denominator:
(x+3) * √(x+3)/(x+3) = 1 * (x+3)
This simplifies to:
√(x+3) = x+3
Step 2: Square both sides to eliminate the square root:
(√(x+3))^2 = (x+3)^2
This simplifies to:
x+3 = (x+3)^2
Step 3: Expand and rearrange the equation:
x + 3 = x^2 + 6x + 9
Step 4: Subtract x and 3 from both sides to get the equation in standard form:
x^2 + 5x + 6 = 0
Step 5: Factor the equation, if possible:
(x+2)(x+3) = 0
Step 6: Set each factor equal to zero and solve for x:
x+2 = 0 or x+3 = 0
This gives us two possible solutions:
x = -2 or x = -3
So, the solutions to the equation are x = -2 and x = -3.
To solve the equation √x+3 / (x+3) = 1 for x, we can follow these steps:
Step 1: Clear the square root by squaring both sides of the equation:
(√x+3 / (x+3))^2 = 1^2
(x+3) / (x+3)^2 = 1
Step 2: Multiply both sides of the equation by (x+3) ^2 to eliminate the fraction:
(x+3) = (x+3)^2
Step 3: Expand the equation on the right side by applying the square of binomial:
x+3 = x^2 + 6x + 9
Step 4: Rearrange the equation by moving all terms to one side to set it equal to zero:
x^2 + 6x + 9 - (x+3) = 0
x^2 + 6x + 9 - x - 3 = 0
x^2 + 5x + 6 = 0
Step 5: Factorize the quadratic equation (if possible):
(x+2)(x+3) = 0
Step 6: Set each factor equal to zero and solve for x:
x + 2 = 0 => x = -2
x + 3 = 0 => x = -3
So, the solutions for x in the equation √x+3 / (x+3) = 1 are x = -2 and x = -3.