How do you simplify (y – x)/(x^2y) + (x + y) (xy^2)?

1 Answer
Apr 21, 2018

See explanation

Explanation:

Rules used:
Negative exponents 1/x^a=x^-a
Exponent of exponent value (a^b)^c=a^(bxxc)
Exponential multiplication a^b*a^c=a^(b+c)
Distributive property a(b+c)=a(b)+a(c)
Zero exponent z^0=1

Steps:
1. Simplify the first half.
Negative exponents (y-x)/(x^2y)=(y-x)*(x^2y)^-1
Exponent of exponent value y(x^-2y^-1)-x(x^-2y^-1)
Distributive property (y-x)(x^-2y^-1)=(x^2y)^-1=x^(2xx(-1))y^-1=x^-2y^-1
Exponential multiplication y^(1-1)x^-2-x^(1-2)y^-1=y^0x^-2-x^-1y^-1
Zero exponent (1)x^-2-x^-1y^-1
Negative exponent 1/x^2-1/(xy)
Result: \color(tomato)(1/x^2-1/(xy))
2. Simplify the second half.
Distributive property (x+y)(xy^2)=x(xy^2)+y(xy^2)
Exponential multiplication x(xy^2)=x^(1+1)y^2=x^2y^2 and y(xy^2)=xy^(1+2)=xy^3
Result: \color(orchid)(x^2y^2+xy^3)
3. Combine these simplified halves.
\color(tomato)(1/x^2-1/(xy))+\color(orchid)(x^2y^2+xy^3)