Question

What is `4/3x^3 - 5/8x^2 +7/9x` when subtracted from `2x^3+3/4x^2-2/9`?

Answer 1

`2/3x^3+11/8x^2-7/9x -2/9`

Explanation:

The most important thing in subtraction is to write the expressions in the correct order.
A subtracted from B means `B-A`
A subtract B means `A -B`

B subtracted from A means `A-B`
B subtract A means `B-A`

Remember that a subtraction involves a change of sign.
Subtracting a number is the same as adding its inverse.

`2x^3+3/4x^2-2/9 color(red)(- (4/3x^3 - 5/8x^2 +7/9x))`

`=2x^3+3/4x^2-2/9 color(red)(-4/3x^3 + 5/8x^2 -7/9x)" "larr`find like terms

`=color(blue)(2x^3-4/3x^3) color(forestgreen)(+3/4x^2 + 5/8x^2)color(mediumpurple)(-7/9x)color(magenta)( -2/9)`

`=color(blue)(2/3x^3) color(forestgreen)(+11/8x^2)color(mediumpurple)(-7/9x)color(magenta)( -2/9)`

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Details of the fraction calculations:
`color(blue)(2-4/3 = 2-1 1/3 = 2/3" "` OR `" "color(blue)(2-4/3 = 6/3-4/3 = 2/3`

`color(forestgreen)(3/4 + 5/8 = 6/8+5/8 = 11/8)`