Question

What is `(3/2+4/7)/((15/8-3/4)-((4+3)/(-4+3))`?

Answer 1

`116/455`(assuming no arithmetic errors on my part)

Explanation:

Given the expression:
`color(white)("XXX")(color(blue)(3/2+4/7))/(color(red)((15/8-3/4))-color(magenta)(((4+3)/(-4/3)))`

Simplifying each component separately:
`color(blue)(3/2+4/7)=21/14+8/14=color(blue)(29/14)`

`color(red)((15/8-3/4))=15/8-6/8=color(red)(9/8)`

`color(magenta)(((4+3)/(-4/3))=7/(-1)=color(magenta)(-7)`

`color(red)((15/8-3/4))-color(magenta)(((4+3)/(-4/3))=color(red)(9/8)-(color(magenta)(-7))=9/8+56/8=color(green)(65/8)`

`(color(blue)(3/2+4/7))/(color(red)((15/8-3/4))-color(magenta)(((4+3)/(-4/3))))=(color(blue)(29/14))/(color(green)(65/8))=color(blue)(29/cancel(14)_7)xxcolor(green)(cancel(8)^4/65)=116/455`