# Simplify 6/a-(7/(a^2))÷(6/(a^3))+7/a

6a-7a2÷6a3+7a
Combine fractions.
Combine fractions with similar denominators.
6+7a+-7a26a3
13a+-7a26a3
13a+-7a26a3
Simplify each term.
Multiply the numerator by the reciprocal of the denominator.
13a-7a2⋅a36
Cancel the common factor of a2.
Move the leading negative in -7a2 into the numerator.
13a+-7a2⋅a36
Factor a2 out of a3.
13a+-7a2⋅a2a6
Cancel the common factor.
13a+-7a2⋅a2a6
Rewrite the expression.
13a-7a6
13a-7a6
Combine -7 and a6.
13a+-7a6
Move the negative in front of the fraction.
13a-7a6
13a-7a6
To write 13a as a fraction with a common denominator, multiply by 66.
13a⋅66-7a6
To write -7a6 as a fraction with a common denominator, multiply by aa.
13a⋅66-7a6⋅aa
Write each expression with a common denominator of a⋅6, by multiplying each by an appropriate factor of 1.
Multiply 13a and 66.
13⋅6a⋅6-7a6⋅aa
Multiply 7a6 and aa.
13⋅6a⋅6-7a⋅a6a
Reorder the factors of a⋅6.
13⋅66a-7a⋅a6a
13⋅66a-7a⋅a6a
Combine the numerators over the common denominator.
13⋅6-7a⋅a6a
Simplify the numerator.
Multiply 13 by 6.
78-7a⋅a6a
Multiply a by a by adding the exponents.
Move a.
78-7(a⋅a)6a
Multiply a by a.
78-7a26a
78-7a26a
78-7a26a
Simplify 6/a-(7/(a^2))÷(6/(a^3))+7/a