Simplify the following expression- m - -m2 - n2-m - -m2 - n2 - m - -m2 - n2-m - -m2 - n2 n2-4m-m2 - n2

m+√(m^2 n^2)m √(m^2 n^2) m √(m^2 n^2)m+√(m^2 n^2)=(m+√(m^2 n^2))^2 (m √(m^2 n^2))^2m^2 m^2+n^2=4m√(m^2 n^2)n^2 (m+√(m^2 n^2)m √(m^2 n^2) m √(m^2 n^2)m ...

You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integration of Irrational Algebraic Fractions - 2

Simplify the ...

Question

Simplify the following expression:
$(\frac{m + \sqrt{m^{2} - n^{2}}}{m - \sqrt{m^{2} - n^{2}}} - \frac{m - \sqrt{m^{2} - n^{2}}}{m + \sqrt{m^{2} - n^{2}}}) \frac{n^{2}}{4 m \sqrt{m^{2} - n^{2}}}$

Open in App

Solution

$\frac{m + \sqrt{m^{2} - n^{2}}}{m - \sqrt{m^{2} - n^{2}}} - \frac{m - \sqrt{m^{2} - n^{2}}}{m + \sqrt{m^{2} - n^{2}}} = \frac{(m + \sqrt{m^{2} - n^{2}})^{2} - (m - \sqrt{m^{2} - n^{2}})^{2}}{m^{2} - m^{2} + n^{2}} = \frac{4 m \sqrt{m^{2} - n^{2}}}{n^{2}}$
$⟹ (\frac{m + \sqrt{m^{2} - n^{2}}}{m - \sqrt{m^{2} - n^{2}}} - \frac{m - \sqrt{m^{2} - n^{2}}}{m + \sqrt{m^{2} - n^{2}}}) \frac{n^{2}}{4 m \sqrt{m^{2} - n^{2}}} = 1$

Suggest Corrections

Similar questions

Q. Simplify:

\frac{m^{2} - n^{2}}{{(m + n)}^{2}} \times \frac{m^{2} + m n + n^{2}}{m^{3} - n^{3}}

Q. Simplify the following expression:

(\frac{1}{(m + n)^{2}} (\frac{1}{m^{2}} + \frac{1}{n^{2}}) + \frac{2}{(m + n)^{3}} (\frac{1}{m} + \frac{1}{n})) m^{2} n^{2}

Q. If

tan θ + sin θ = m

and

tan θ - sin θ = n,

then which of the following relation between

m, n

is correct?

Q. Simlify:

\frac{m^{2} - n^{2}}{{(m + n)}^{2}} \times \frac{m^{2} + m n + n^{2}}{m^{3} - n^{3}}

Q. Simplify the following expression:

(m + n - \frac{4 m n}{m + n}) : (\frac{m}{m + n} - \frac{n}{n - m} - \frac{2 m n}{m^{2} - n^{2}})

Join BYJU'S Learning Program

Simplify the following expression:(m+√m2−n2m−√m2−n2−m−√m2−n2m+√m2−n2)n24m√m2−n2

m+√m2−n2m−√m2−n2−m−√m2−n2m+√m2−n2=(m+√m2−n2)2−(m−√m2−n2)2m2−m2+n2=4m√m2−n2n2⟹(m+√m2−n2m−√m2−n2−m−√m2−n2m+√m2−n2)n24m√m2−n2=1

Simplify the following expression:
$(\frac{m + \sqrt{m^{2} - n^{2}}}{m - \sqrt{m^{2} - n^{2}}} - \frac{m - \sqrt{m^{2} - n^{2}}}{m + \sqrt{m^{2} - n^{2}}}) \frac{n^{2}}{4 m \sqrt{m^{2} - n^{2}}}$