simplify 3upon 5-√3 +2 upon 5+√3
Answers
Solution!!
3/(5 - √3) + 2/(5 + √3)
Rationalise the denominator of the first fraction.
= 3/(5 - √3) × (5 + √3)/(5 + √3) + 2/(5 + √3)
= [3(5 + √3)/(5 - √3)(5 + √3)] + 2/(5 + √3)
Simplify using (a - b)(a + b) = a² - b².
= [3(5 + √3)/(5)² - (√3)²] + 2/(5 + √3)
= [3(5 + √3)/(25 - 3)] + 2/(5 + √3)
= 3(5 + √3)/22 + 2/(5 + √3)
Distribute 3 through the parentheses.
= [(15 + 3√3)/22] + 2/(5 + √3)
Rationalise the denominator of the second fraction.
= [(15 + 3√3)/22] + 2/(5 + √3) × (5 - √3)/(5 - √3)
= [(15 + 3√3)/22] + 2(5 - √3)/(5 + √3)(5 - √3)
Simplify using (a + b)(a - b) = a² - b².
= [(15 + 3√3)/22] + [2(5 - √3)/(5)² - (√3)²]
= [(15 + 3√3)/22] + 2(5 - √3)/(25 - 3)
= [(15 + 3√3)/22] + 2(5 - √3)/(22)
Distribute 2 through the parentheses.
= [(15 + 3√3)/22] + [(10 - 2√3)/(22)]
Calculate the sum as the denominator is same.
= (15 + 3√3 + 10 - 2√3)/22
Group the like term.
= (15 + 10 + 3√3 - 2√3)/22
Calculate the sum.
= (25 + √3)/22