For the equation, a. Write the value or values of the variable that make a denominator zero.

vazelinahS

vazelinahS

Answered question

2021-06-03

For the equation,

a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable.

b. Keeping the restrictions in mind, solve the equation.
4x+5+2x5=32x225

Answer & Explanation

Caren

Caren

Skilled2021-06-04Added 96 answers

Step 1
we have to find the following things
(a)The values of x at which denominator is not defined.
(b)we have to solve the equation
Given: 4x+5+2x5=32x225
Step 2
4x+5+2x5=32x225
here we can see x=5 and x=-5 are the
values of x for which the denominator is zero.
(a)x=5 and x=-5
(b)we will take the LCM
4(x5)+2(x+5)(x+5)(x5)=32x225
4x20+2x+10x225=32x225
6x10x225=32x225
now as x5,5
at x=5,-5 the function is not defined.
6x10=32
6x=42
x=7
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

Vasquez

Vasquez

Expert2023-06-17Added 669 answers

a. We must identify the values of the variable that result in zero denominators in order to find the limits on the variable.
The restrictions are:
x+5=0 and x5=0
Solving these equations, we find:
x=5 and x=5
b. Now, let's solve the equation while keeping the restrictions in mind.
4x+5+2x5=32x225
To proceed, we'll multiply the entire equation by (x+5)(x5) to eliminate the denominators:
4(x5)+2(x+5)=32
Simplifying the equation further:
4x20+2x+10=32
6x10=32
6x=42
x=7
Therefore, the solution to the equation, considering the restrictions, is x=7.
Don Sumner

Don Sumner

Skilled2023-06-17Added 184 answers

Answer:
x=3013
Explanation:
The given equation is:
4x+5+2x5=32x225
To solve this equation, we need to follow these steps:
a. Identify the values of the variable that make a denominator zero. These values will be the restrictions on the variable.
To find the restrictions, we set the denominators of the fractions equal to zero and solve for x:
For the first fraction, the denominator is zero when:
x+5=0
Solving for x, we have:
x=5
For the second fraction, the denominator is zero when:
x5=0
Solving for x, we have:
x=5
Therefore, the restrictions on the variable are x=5 and x=5.
b. Now, let's solve the equation, keeping the restrictions in mind.
To do this, we'll start by multiplying the entire equation by (x225) to eliminate the fractions:
(x225)·(4x+5+2x5)=(x225)·32x225
Simplifying:
4(x225)+2(x225)=32
Expanding and combining like terms:
4x2100+2x250=32
6x2150=32
Rearranging the equation:
6x2=32+150
6x2=182
Dividing both sides by 6:
x2=1826
x2=3013
Taking the square root of both sides:
x=±3013
However, we need to check if these solutions satisfy the restrictions we found earlier. Since x=5 and x=5 are not solutions to the equation (they make the denominators zero), we only consider the solutions within the restrictions.
Therefore, the final solution is:
x=3013
nick1337

nick1337

Expert2023-06-17Added 777 answers

Step 1:
a. To find the restrictions on the variable, we need to identify the values of x that would make any of the denominators zero. In this equation, we have two denominators: (x + 5) and (x - 5).
To make the first denominator zero, we set (x + 5) equal to zero and solve for x:
x+5=0
x=5
To make the second denominator zero, we set (x - 5) equal to zero and solve for x:
x5=0
x=5
Therefore, the restrictions on the variable x are x ≠ -5 and x ≠ 5.
Step 2:
b. Now let's solve the equation by keeping the restrictions in mind.
4x+5+2x5=32x225
First, let's simplify the right side by factoring the denominator:
4x+5+2x5=32(x+5)(x5)
Next, let's find a common denominator for the left side of the equation, which is (x + 5)(x - 5):
4(x5)(x+5)(x5)+2(x+5)(x+5)(x5)=32(x+5)(x5)
Combining the fractions on the left side:
4x20+2x+10(x+5)(x5)=32(x+5)(x5)
Simplifying the numerator:
6x10(x+5)(x5)=32(x+5)(x5)
Now, we can eliminate the denominators by multiplying both sides of the equation by (x + 5)(x - 5):
(x+5)(x5)·6x10(x+5)(x5)=(x+5)(x5)·32(x+5)(x5)
Simplifying:
6x10=32
Next, let's isolate the variable by moving the constant term to the other side:
6x=32+10
6x=42
Finally, solve for x by dividing both sides of the equation by 6:
x=426
x=7
Therefore, the solution to the equation is x=7, but we need to remember the restrictions on the variable x, which are x5 and x5.
Hence, the final solution, considering the restrictions, is x=7.

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