SOLUTION: If {( x-sqrt24)(sqrt75 + sqrt 50)}/ ( sqrt75 - sqrt50) = 1 , then what is the value of x. please solve it..

Question 919074: If {( x-sqrt24)(sqrt75 + sqrt 50)}/ ( sqrt75 - sqrt50) = 1 , then what is the value of x. please solve it..
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

your solution is shown below.
the solution is that x = 5

step 1 shows the original problem.

step 2 multiplies both sides of the equation by (sqrt(75) - sqrt(50)).

step 3 divides both sides of the equation by (sqrt(75) + sqrt(50)).

step 4 multiplies numerator and denominator of the expression on the right by (sqrt(75 - sqrt(50).
this rationalizes the denominator and allows further simplification of the problem.

step 5 performs the multiplications indicated.

step 6 simplifies the results from step 5.

step 7 simplifies the results even further by simplifying the radicals to get sqrt(75) = 5*sqrt(3) and sqrt(50) = 5*sqrt(2)

step 8 simplifies the results even further by combining like terms and translating sqrt(3) * sqrt(2) into sqrt(6).

step 9 simplifies the results even further by performing by dividing (125 - 50*sqrt(6) by 25.

step 10 adds sqrt(24) to both sides of the equation.

step 11 simplifies sqrt(24) to make it equal to 2*sqrt(6)

step 12 combines like terms to make -2*sqrt(6) and +2*sqr5(6) = 0 and therefore cancel out to get the result of x = 5.

that's your solution.

it has been confirmed through the use of my calculator that the solution is correct.

$$$

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