What you have is a product that doesn't support Windows 8.1. The new Mathway is using online browser instead of downloaded applications. For additional information about the problems calculated, you will have to pay for a subscription.
However, if you have the package, right click it and choose Compatibility > Windows XP. If it doesn't work, then the web version needs to be used.
Subscription plans: https://mathway.zendesk.com/hc/en-us/articles/200353317-Subscribing-to-mathway
The service is free, but additional premium features require to be purchased.