Subtracting Polynomials: A StepbyStep Guide
This article will guide you through the process of subtracting the polynomial (6/5)x²  (4/5)x³ + (5/6) + (3/2)x from the polynomial (1/3)x³  (5/2)x² + (3/5)x + (1/4).
Understanding the Process
Subtracting polynomials involves combining like terms after distributing the negative sign to all terms within the second polynomial. Let's break down the steps:

Rewrite the expression:
 Begin by writing the expression as: (1/3)x³  (5/2)x² + (3/5)x + (1/4)  [(6/5)x²  (4/5)x³ + (5/6) + (3/2)x]

Distribute the negative sign:
 Multiply each term inside the brackets by 1. (1/3)x³  (5/2)x² + (3/5)x + (1/4)  (6/5)x² + (4/5)x³  (5/6)  (3/2)x

Combine like terms:
 Group together terms with the same variable and exponent. [(1/3)x³ + (4/5)x³] + [(5/2)x²  (6/5)x²] + [(3/5)x  (3/2)x] + [(1/4)  (5/6)]

Simplify each group:
 Find a common denominator for each group of like terms and perform the addition or subtraction. [(5/15)x³ + (12/15)x³] + [(25/10)x²  (12/10)x²] + [(6/10)x  (15/10)x] + [(3/12)  (10/12)]

Final Result:
 Combine the simplified terms to get the final result. (17/15)x³  (37/10)x²  (9/10)x  (7/12)
Conclusion
Subtracting polynomials involves careful attention to signs and combining like terms. By following the steps outlined above, you can confidently subtract any two polynomials.