Simplify the expression: (m+b)/(m-b) + (m-b)/(m+b) − (m2+b2)/(m2-b2)

Question

ScanSolve AI Tutor · Accepted Answer

Here's the step-by-step solution:

The given expression is:

\frac{m+b}{m-b} + \frac{m-b}{m+b} - \frac{m^2+b^2}{m^2-b^2}

Find a common denominator for the first two terms.
The common denominator is $(m-b)(m+b) = m^2-b^2$ .
$\frac{(m+b)^2}{(m-b)(m+b)} + \frac{(m-b)^2}{(m+b)(m-b)} - \frac{m^2+b^2}{m^2-b^2}$ $\frac{(m+b)^2 + (m-b)^2}{m^2-b^2} - \frac{m^2+b^2}{m^2-b^2}$
Expand the squares in the numerator.
Recall that $(A+B)^2 = A^2 + 2AB + B^2$ and $(A-B)^2 = A^2 - 2AB + B^2$ .
$\frac{(m^2 + 2mb + b^2) + (m^2 - 2mb + b^2)}{m^2-b^2} - \frac{m^2+b^2}{m^2-b^2}$
Combine like terms in the numerator.
The $2mb$ and $-2mb$ terms cancel out.
$\frac{m^2 + m^2 + b^2 + b^2}{m^2-b^2} - \frac{m^2+b^2}{m^2-b^2}$ $\frac{2m^2 + 2b^2}{m^2-b^2} - \frac{m^2+b^2}{m^2-b^2}$
Since both terms now have the same denominator, combine their numerators.
$\frac{(2m^2 + 2b^2) - (m^2+b^2)}{m^2-b^2}$
Distribute the negative sign in the numerator and combine like terms.
$\frac{2m^2 + 2b^2 - m^2 - b^2}{m^2-b^2}$ $\frac{(2m^2 - m^2) + (2b^2 - b^2)}{m^2-b^2}$ $\frac{m^2 + b^2}{m^2-b^2}$

Simplify the expression: (m+b)/(m-b) + (m-b)/(m+b) - (m2+b2)/(m2-b2)