How do you simplify #(1/sqrt(a-1)+sqrt(a+1))/(1/sqrt(a+1)-1/sqrt(a-1))div sqrt(a+1)/((a-1)sqrt(a+1)-(a+1)sqrt(a-1)),# a>1 ?
2 Answers
Huge math formatting...
Explanation:
#color(blue)(((1/sqrt(a-1)+sqrt(a+1))/(1/sqrt(a+1)-1/sqrt(a-1)))/ (sqrt(a+1)/((a-1)sqrt(a+1)-(a+1)sqrt(a-1)))#
#=color(red)(((1/sqrt(a-1)+sqrt(a+1))/((sqrt(a-1)-sqrt(a+1))/(sqrt(a+1) cdot sqrt(a-1))))/ (sqrt(a+1)/(sqrt(a-1) cdot sqrt(a-1) cdot sqrt(a+1)-sqrt(a+1) cdot sqrt(a+1)sqrt(a-1)))#
#=color(blue)(((1/sqrt(a-1)+sqrt(a+1))/((sqrt(a-1)-sqrt(a+1))/(sqrt(a+1) cdot sqrt(a-1))))/ (sqrt(a+1)/(sqrt(a+1) cdot sqrt(a-1)(sqrt(a-1)-sqrt(a+1)))#
#=color(red)((1/sqrt(a-1)+sqrt(a+1))/((sqrt(a-1)-sqrt(a+1))/(sqrt(a+1) cdot sqrt(a-1)))xx(sqrt(a+1) cdot sqrt(a-1)(sqrt(a-1)-sqrt(a+1)))/sqrt(a+1)#
#=color(blue)((1/sqrt(a-1)+sqrt(a+1))xx((sqrt(a+1) cdot sqrt(a-1))/(sqrt(a-1)-sqrt(a+1)))xx(cancel((sqrt(a+1))) cdot sqrt(a-1)(sqrt(a-1)-sqrt(a+1)))/cancelsqrt(a+1))#
#=color(red)(((1+sqrt(a+1) cdot sqrt(a-1))/(sqrt(a-1)))xx((sqrt(a+1) cdot sqrt(a-1))/(sqrt(a-1)-sqrt(a+1)))xx sqrt(a-1)cdot(sqrt(a-1)-sqrt(a+1))#
#=color(blue)(((1+sqrt(a+1) cdot sqrt(a-1))/cancel(sqrt(a-1)))xx((sqrt(a+1) cdot cancel((sqrt(a-1))))/color(red)(cancel(color(green)((sqrt(a-1)-sqrt(a+1)))))xx sqrt(a-1)cdot color(red)(cancel color(green)((sqrt(a-1)-sqrt(a+1)))#
#=color(red)(ul(bar(|color(blue)((1+sqrt(a+1) cdot sqrt(a-1))cdot(sqrt((a+1)(a-1))))|#
Explanation:
To simplify things greatly we will use