Question

How to simplify?

(x^2y+xy^2)/(y^2+2/5xy)

Answer 1

x2/2x2-5xy+2y2*2x2y-xy2/(2xy2)2

Final result :

2x5y2 + 16x3y5 - 20x2y3 - 1

———————————————————————————

4xy2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(x2) (y2)

(((————•(x2))-5xy)+((((2•(y2))•2)•(x2))•y))-(x•—————————)

2 ((2xy2)2)

Step 2 :

y2

Simplify ——————

22x2y4

Dividing exponential expressions :

2.1 y2 divided by y4 = y(2 - 4) = y(-2) = 1/y2

Equation at the end of step 2 :

(x2) 1

(((————•(x2))-5xy)+((((2•(y2))•2)•(x2))•y))-(x•—————)

2 4x2y2

Step 3 :

Equation at the end of step 3 :

(x2) 1

(((————•(x2))-5xy)+(((2y2•2)•x2)•y))-————

2 4xy2

Step 4 :

Multiplying exponents :

4.1 21 multiplied by 21 = 2(1 + 1) = 22

Equation at the end of step 4 :

(x2) 1

(((————•(x2))-5xy)+((22y2•x2)•y))-————

2 4xy2

Step 5 :

x2

Simplify ——

2

Equation at the end of step 5 :

x2 1

(((—— • x2) - 5xy) + 22x2y3) - ————

2 4xy2

Step 6 :

Multiplying exponential expressions :

6.1 x2 multiplied by x2 = x(2 + 2) = x4

Equation at the end of step 6 :

x4 1

((—— - 5xy) + 22x2y3) - ————

2 4xy2

Step 7 :

Rewriting the whole as an Equivalent Fraction :

7.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 2 as the denominator :

5xy 5xy • 2

5xy = ——— = ———————

1 2