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Simplify the expression and solve the equation. Show all calculations

Simplify the expression and solve the equation. Show all calculations-example-1
User Khylo
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First of all, we can observe that


√(18) = √(2\cdot 9)=√(2)\cdot√(9)=3√(2)

Then, we can rationalize the denominator by using the formula


(a-b)(a+b)=a^2-b^2

If we multiply both numerator and denominator by [/tex]\sqrt{8}+3[/tex] we have


(3√(2))/(√(8)-3)\cdot(√(8)+3)/(√(8)+3)=(3√(2)(√(8)+3))/(-1) = -3√(2)(√(8)+3)

We can also observe that


√(8) = √(2\cdot 4)=√(2)\cdot√(4)=2√(2)

And the expression simplifies into


-3√(2)(2√(2)+3) =-12-9√(2) = -3(4+3√(2))

User LRLucena
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