How to scale an object to an exact ratio?

9/7= 1.28   7/4.3=1.62 ths aspect ratio are off.    So your 1.62 aspect ratio is wider the 9:7  1.28 aspect ratio. If you were to resize your Image to fill the narrower image's aspect ratio height  the left and right sides if you image would be clipped off. My Batch Mockup script edit option(s) can pe user to populate you 7:4.3 images into the 9:7 object are  fitted to the area where tout image will have boarders top and bottom  Ot the fill the 9:7  area where the left and right sides will be clipped off.  To help you visualize this I  include this image.     The red rectangle is the  9:7 aspect area.  The green your 7:4.3 Image fitted to the area you see the boarders top and bottom inside the red area.  The Blue rectangle your image resized to fill the 9:7 height you can see the left and right clip off areas outside the res area.

You do not scale to Aspect Ratios you crop or distort to a different aspect ratio.  Adobe prefers to call it content aware scale (Alt+Shift+Ctrl+C) I prefer content aware distort.   I do not automate distortion just Fit and Crop.

Why Adobe content aware scale. Changind Aspect Ratio like  2:3 to 3:2 thing like going from Portrait to Landscape just do not produce acceptable results.

Not really. 

You could create a planar guide/grid that encompasses both ratios, then convert it to a Smart Object and perspectively transform it to meet the existing one and the intended one should become more or less clear …  

Then you can stitch together and touch up a version of the book-image that corresponds to that.