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Exercise

$\frac{1}{2-\sqrt{x}}$

Step-by-step Solution

1

Multiply and divide the fraction $\frac{1}{2-\sqrt{x}}$ by the conjugate of it's denominator $2-\sqrt{x}$

$\frac{1}{2-\sqrt{x}}\frac{2+\sqrt{x}}{2+\sqrt{x}}$
2

Multiplying fractions $\frac{1}{2-\sqrt{x}} \times \frac{2+\sqrt{x}}{2+\sqrt{x}}$

$\frac{2+\sqrt{x}}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}$
3

Solve the product of difference of squares $\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)$

$\frac{2+\sqrt{x}}{4-x}$

Final answer to the exercise

$\frac{2+\sqrt{x}}{4-x}$

Try other ways to solve this exercise

  • Choose an option
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
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Similar Questions Solved

$\frac{3}{5+\sqrt{3}}$

$\frac{1}{2+\sqrt{3}}$

$\frac{2}{\sqrt{5}-\sqrt{3}}$

$\frac{5}{2+\sqrt{3}}$

$\frac{3}{\sqrt{7}-2}$

$\frac{2}{3+\sqrt{3}}$

$\frac{5}{\sqrt{7}}$

Main Topic: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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