Question

5/x^2-7x+12 + 2/x-3 = 5/x-4

Answer 1

Check the solution

Answer 2

If I were a student posting math questions on here, I would not trust the
bot to get you the correct answer. e.g. this one .....

5/(x^2-7x+12) + 2/(x-3) = 5/(x-4) , where x ≠ 3,4
5/((x-3)(x-4)) + 2/(x-3) = 5/(x-4)
multiply each side by (x-3)(x-4)
5 + 2(x-4) = 5(x-3)
5 + 2x - 8 = 5x - 15
12 = 3x
x = 4

but x ≠ 4, so there is no solution

(but not for the reason that the bot stated , since it couldn't solve the equation properly)

Answer 3

To solve the equation 5/x^2-7x+12 + 2/x-3 = 5/x-4:

First, factor the denominator of the first fraction: x^2-7x+12 = (x-3)(x-4)

Second, rewrite the equation with a common denominator:

5/(x-3)(x-4) + 2/(x-3) = 5/(x-4)

Third, simplify the left side using the common denominator:

(5+2(x-4))/(x-3)(x-4) = 5/(x-4)

Fourth, multiply both sides by (x-4) to eliminate the denominator on the right side:

5+2(x-4) = 5(x-3)

Fifth, simplify and solve for x:

5+2x-8 = 5x-15

-3x = -2

x = 2/3

Therefore, the solution to the equation is x = 2/3.

Answer 4

To check the solution, we need to substitute x = 2/3 into the original equation and see if both sides are equal.

5/x^2-7x+12 + 2/x-3 = 5/x-4

Substituting x = 2/3, we get:

5/(2/3)^2 - 7(2/3) + 12 + 2/(2/3 - 3) = 5/(2/3 - 4)

Simplifying, we get:

5/(4/9) - 14/3 + 12 + 2/(-2 1/3) = 5/(-10/3)

20/4 - 14/3 + 12 - 6/7 = -15/2

5 - 56/21 + 252/21 - 18/7 = -15/2

35/21 - 56/21 = -15/2

-21/21 = -15/2 (not true)

Thus, the solution x = 2/3 does not make the equation true, which means there is no solution to the equation.

Answer 5

Thank you for bringing this to my attention. As an AI language model, my responses are based on pre-existing algorithms and statistical patterns in data. However, I strive to provide accurate and helpful responses to the best of my abilities. I appreciate any feedback or corrections to ensure that I am providing the most reliable assistance possible.