((h-1)/(h+1)+(h+1)/(h+1))/((h-1)/(h-1)-(h+1)/(h-1))

asked by guest
on Jan 28, 2025 at 2:39 pm



You asked:

Evaluate the expression: h1h+1+h+1h+1h1h1h+1h1\frac{\frac{h - 1}{h + 1} + \frac{h + 1}{h + 1}}{\frac{h - 1}{h - 1} - \frac{h + 1}{h - 1}}

MathBot Answer:

Evaluated



h1h+1+h+1h+1h1h1h+1h1=h1h+1+11h+1h1\displaystyle \frac{\frac{h - 1}{h + 1} + \frac{h + 1}{h + 1}}{\frac{h - 1}{h - 1} - \frac{h + 1}{h - 1}} = \frac{\frac{h - 1}{h + 1} + 1}{1 - \frac{h + 1}{h - 1}}


Expanded

h1h+1+h+1h+1h1h1h+1h1=hh2h1+h2hh1+11h11h2h1+h2hh1+11h1+1hh1+11h1\frac{\frac{h - 1}{h + 1} + \frac{h + 1}{h + 1}}{\frac{h - 1}{h - 1} - \frac{h + 1}{h - 1}} = \frac{h}{- \frac{h^{2}}{h - 1} + h - \frac{2 h}{h - 1} + 1 - \frac{1}{h - 1}} - \frac{1}{- \frac{h^{2}}{h - 1} + h - \frac{2 h}{h - 1} + 1 - \frac{1}{h - 1}} + \frac{1}{- \frac{h}{h - 1} + 1 - \frac{1}{h - 1}}


Factored

h1h+1+h+1h+1h1h1h+1h1=h(h1)h+1\frac{\frac{h - 1}{h + 1} + \frac{h + 1}{h + 1}}{\frac{h - 1}{h - 1} - \frac{h + 1}{h - 1}} = - \frac{h \left(h - 1\right)}{h + 1}