What is the answer to (((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1 ?

The answer to (((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1 is x=4,x=16

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(((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1

Solution

\frac{( ( 9 - x ) ( 3 - x ) )}{( 3 + x )} = 1

Solution

x = 4, x = 16

Solution steps

\frac{( ( 9 - x ) ( 3 - x ) )}{( 3 + x )} = 1

Multiply both sides by

3 + x

\frac{( 9 - x ) ( 3 - x )}{3 + x} (3 + x) = 1 \cdot (3 + x)

Simplify

(9 - x) (3 - x) = 3 + x

Expand

(9 - x) (3 - x) : 27 - 9 x - 3 x + x x

27 - 9 x - 3 x + x x = 3 + x

Factor

27 - 9 x - 3 x + x x : (x - 3) (x - 9)

(x - 3) (x - 9) = 3 + x

Expand

(x - 3) (x - 9) : x x - 9 x - 3 x + 27

x x - 9 x - 3 x + 27 = 3 + x

Move

3 x

to the right side

x x - 9 x + 27 = 3 + x + 3 x

Move

27

to the right side

x x - 9 x = 3 x + x - 24

Move

x

to the left side

x x - 10 x = 3 x - 24

Factor

x x - 10 x : x (x - 10)

x (x - 10) = 3 x - 24

Divide both sides by

x - 10

x = \frac{3 x - 24}{x - 10}

Square both sides:

x = \frac{9 x ^{2} - 144 x + 576}{x ^{2} - 20 x + 100}

x = \frac{9 x ^{2} - 144 x + 576}{x ^{2} - 20 x + 100}

Solve

x = \frac{9 x ^{2} - 144 x + 576}{x ^{2} - 20 x + 100} : x = 4, x = 9, x = 16

x = 4, x = 9, x = 16

Verify Solutions:

x = 4

True

, x = 9

False

, x = 16

True

The solutions are

x = 4, x = 16

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Frequently Asked Questions (FAQ)

What is the answer to (((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1 ?
The answer to (((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1 is x=4,x=16
Solve for x: (((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1
The solution is x=4,x=16

(((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to (((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1 ?

Solve for x: (((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1