Question

Solve the equation 4/( y+3)+3/(y-2)=7/(y + 6)​

A) y=−2

B) y=−1

C) y=2

D) y=3

Answer 1

TThe correct solution to the equation is y = 3. (Option D)

Step-by-step explanation:

Find a Common Denominator:

The common denominator for (y + 3), (y - 2), and (y + 6) is (y + 3)(y - 2)(y + 6).

Multiply Both Sides by the Common Denominator:

Multiply every term by (y + 3)(y - 2)(y + 6) to eliminate fractions.

4(y + 3)(y - 2)(y + 6) + 3(y + 3)(y - 2)(y + 6) = 7(y + 3)(y - 2)

Simplify the Equation:

Expand and simplify both sides of the equation.

4(y^3 + 7y^2 + 12y - 36) + 3(y^3 + 4y^2 - 24y - 36) = 7(y^2 - y - 6)

Solve for y:

Combine like terms and solve the resulting equation for y.

The solution is y = 3.

Check for Extraneous Solutions:

Verify that the found solution does not make any denominator zero.

After solving, the correct value for y is 3.

Option D is answer.