Question

(a^2 x^2+25y^2)/(ax-5y)+10axy/(5y-ax)

Answer 1

(a^2 x^2+25y^2)/(ax-5y)+10axy/(5y-ax)
a²x²+25y²/ax-5y+10axy/-(ax-5y)
a²x²+25y²/ax-5y+10axy/ax-5y
a²x²+25y²+10axy/ax-5y
a²x²-10axy+25y²/ax-5y
(ax-5y)²/ax-5y
ax-5y

Answer 2

To simplify the expression (a^2x^2 + 25y^2)/(ax - 5y) + 10axy/(5y - ax), we'll first find a common denominator and then combine the fractions. The common denominator is (ax - 5y)(5y - ax). Let's proceed with the simplification:

Step 1: Find the common denominator. Common denominator = (ax - 5y)(5y - ax)

Step 2: Adjust the numerators to have the common denominator. The first fraction's numerator is a^2x^2 + 25y^2. To get the common denominator, we'll multiply the first term by (5y - ax) and the second term by (ax - 5y): a^2x^2(5y - ax) + 25y^2(ax - 5y)

The second fraction's numerator is 10axy. To get the common denominator, we'll multiply the numerator by (ax - 5y): 10axy(ax - 5y)

Step 3: Combine the fractions. Now that both fractions have the common denominator, we can add them: (a^2x^2(5y - ax) + 25y^2(ax - 5y))/(ax - 5y)(5y - ax) + 10axy(ax - 5y)/(ax - 5y)(5y - ax)

Step 4: Combine the numerators. (a^2x^2(5y - ax) + 25y^2(ax - 5y) + 10axy(ax - 5y))/(ax - 5y)(5y - ax)

Step 5: Simplify further. Now, let's simplify the numerator further by expanding the expressions: a^2x^2 * 5y - a^2x^3 + 25y^2ax - 25y^3 + 10a^2xy^2 - 50axy^2

Combine like terms:

• a^2x^3 + 25y^2ax + 10a^2xy^2 - 50axy^2 + a^2x^2 * 5y - 25y^3

The final simplified expression is: (-a^2x^3 + 25y^2ax + 10a^2xy^2 - 50axy^2 + a^2x^2 * 5y - 25y^3)/(ax - 5y)(5y - ax)