The equation of a curve is given by \( y=a b^{x} \), where \( a \) and \( b \) are constants. Given that the curve passes through \( (1,21),(2,63) \) and \( (k, 189) \), find the values of \( a, b \) and \( k \).

a) \( \quad x^{2}=49 \)

Perform the indicated operation. \( \frac{8}{x^{2}-2 x-35}+\frac{7}{x-7} \) \( \frac{8}{x^{2}-2 x-35}+\frac{7}{x-7}=\square( \) Simplify your answer. \( ) \)

Considera la igualdad \( \mathrm{P}=\frac{\mathrm{n}-1}{\mathrm{n}+1} \), con n un número entero. ¿Para cuántos valores distintos de n se cumple que P es un número entero?

\( \frac{\frac{\frac{2}{x}}{\frac{2}{x^{2}}+\frac{7}{x}}}{\frac{\frac{2}{x}}{\frac{2}{x^{2}}+\frac{7}{x}}=\square \text { (Simplify your answer.) }} \)

Reste \( 2 x^{2}-7 x-1 \) de la suma de \( x^{2}+9 x-4 \) y \( -5 x^{2}-7 x+10 \)