# Simplify 4/3a^2+2/5a-1/2a^2-4/3a

43a2+25a-12a2-43a
Simplify each term.
Combine 43 and a2.
4a23+25a-12a2-43a
Combine 25 and a.
4a23+2a5-12a2-43a
Combine a2 and 12.
4a23+2a5-a22-43a
Combine a and 43.
4a23+2a5-a22-a⋅43
Move 4 to the left of a.
4a23+2a5-a22-4a3
4a23+2a5-a22-4a3
To write 4a23 as a fraction with a common denominator, multiply by 22.
2a5+4a23⋅22-a22-4a3
To write -a22 as a fraction with a common denominator, multiply by 33.
2a5+4a23⋅22-a22⋅33-4a3
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 4a23 and 22.
2a5+4a2⋅23⋅2-a22⋅33-4a3
Multiply 3 by 2.
2a5+4a2⋅26-a22⋅33-4a3
Multiply a22 and 33.
2a5+4a2⋅26-a2⋅32⋅3-4a3
Multiply 2 by 3.
2a5+4a2⋅26-a2⋅36-4a3
2a5+4a2⋅26-a2⋅36-4a3
Combine the numerators over the common denominator.
2a5+4a2⋅2-a2⋅36-4a3
Simplify each term.
Simplify the numerator.
Factor a2 out of 4a2⋅2-a2⋅3.
Factor a2 out of 4a2⋅2.
2a5+a2(4⋅2)-a2⋅36-4a3
Factor a2 out of -a2⋅3.
2a5+a2(4⋅2)+a2(-1⋅3)6-4a3
Factor a2 out of a2(4⋅2)+a2(-1⋅3).
2a5+a2(4⋅2-1⋅3)6-4a3
2a5+a2(4⋅2-1⋅3)6-4a3
Multiply 4 by 2.
2a5+a2(8-1⋅3)6-4a3
Multiply -1 by 3.
2a5+a2(8-3)6-4a3
Subtract 3 from 8.
2a5+a2⋅56-4a3
2a5+a2⋅56-4a3
Move 5 to the left of a2.
2a5+5a26-4a3
2a5+5a26-4a3
To write 2a5 as a fraction with a common denominator, multiply by 33.
5a26+2a5⋅33-4a3
To write -4a3 as a fraction with a common denominator, multiply by 55.
5a26+2a5⋅33-4a3⋅55
Write each expression with a common denominator of 15, by multiplying each by an appropriate factor of 1.
Multiply 2a5 and 33.
5a26+2a⋅35⋅3-4a3⋅55
Multiply 5 by 3.
5a26+2a⋅315-4a3⋅55
Multiply 4a3 and 55.
5a26+2a⋅315-4a⋅53⋅5
Multiply 3 by 5.
5a26+2a⋅315-4a⋅515
5a26+2a⋅315-4a⋅515
Combine the numerators over the common denominator.
5a26+2a⋅3-4a⋅515
Simplify each term.
Simplify the numerator.
Factor 2a out of 2a⋅3-4a⋅5.
Factor 2a out of 2a⋅3.
5a26+2a(3)-4a⋅515
Factor 2a out of -4a⋅5.
5a26+2a(3)+2a(-2⋅5)15
Factor 2a out of 2a(3)+2a(-2⋅5).
5a26+2a(3-2⋅5)15
5a26+2a(3-2⋅5)15
Multiply -2 by 5.
5a26+2a(3-10)15
Subtract 10 from 3.
5a26+2a⋅-715
5a26+2a⋅-715
Multiply -7 by 2.
5a26+-14a15
Move the negative in front of the fraction.
5a26-14a15
5a26-14a15
Simplify 4/3a^2+2/5a-1/2a^2-4/3a

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