# 1. solve the equation and check ur solution. 2/(x-4)(x-2) = 1/x-4 + 2/x-2 2. simplyfy the expression 3x^(1/3) - x^(-2/3) / 3x^(-2/3) 3. simplyfy the comlex fraction. x(under squareroot) - 1/ 2x(x under square root) / x(x under squareroot).

1. solve the equation and check ur solution. 2/(x-4)(x-2) = 1/x-4 + 2/x-2
2. simplyfy the expression $3{x}^{1/3}-{x}^{-2/3}/3{x}^{-2/3}$
3. simplyfy the comlex fraction. x(under squareroot) - 1/ 2x(x under square root) / x(x under squareroot).
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lelapem
1. $\frac{2}{\left(x-4\right)\left(x-2\right)}=\frac{1}{x-4}+\frac{2}{x-2}$
Get a common denominator on the right side of the equation
$\frac{2}{\left(x-4\right)\left(x-2\right)}=\left(\frac{1}{x-4}\right)\left(\frac{x-2}{x-2}\right)+\left(\frac{2}{x-2}\right)\left(\frac{x-4}{x-4}\right)$
Simplify
$\frac{2}{\left(x-4\right)\left(x-2\right)}=\frac{x-2}{\left(x-4\right)\left(x-2\right)}+\frac{2\left(x-4\right)}{\left(x-4\right)\left(x-2\right)}$
Now the denominators will all cancel if you multiply bothsides of the equation by (x-4)(x-2). Just be sure your answer does not include 4 or 2 because that would make your originaldenominator 0. You are left to solve:
2 = x - 2 + 2(x-4)
2. If you have a negative exponent in thedenominator of your fraction, it can be brought up to the numerator as a positive exponent. So the original problem becomes $\frac{{x}^{\frac{2}{3}\left(3{x}^{\frac{1}{3}}-{x}^{\frac{-2}{3}}\right)}}{3}$ o depending on whether there were parentheses around the 3x in the denominator. Now just multiply and use yourexponent rules.
3. $\frac{\sqrt{x}-\frac{1}{2\sqrt{x}}}{\sqrt{x}}=\frac{1}{\sqrt{x}}\left(\sqrt{x}-\frac{1}{2\sqrt{x}}\right)$ Multiply through and simplify.