To eliminate the denominators in the equation (2/x)+(4/x+9) = 9, we multiply each side by the lowest common denominator, ______ to get the equivalent equation _______.
I know the first blank is x^2 + 9x, but I can't figure out the second one. I put [-3 (3x^2 - 25x + 6)]/ x^2 + 9x but it said that answer was wrong. pls help
2(x+9) + 4x = 9x(x+9)
or expand it out
To eliminate the denominators in the equation (2/x) + (4/(x+9)) = 9, we need to find the lowest common denominator (LCD) for the fractions.
The LCD is the least common multiple (LCM) of the denominators, which in this case are x and (x+9).
To find the LCM, we factorize the denominators and take the highest power of each prime factor:
Denominator x: Prime factorization = x
Denominator (x+9): Prime factorization = (x+9)
The LCM of x and (x+9) is the product of the highest powers of each prime factor, which in this case is x(x+9).
Now, we multiply each term in the equation by the LCD x(x+9) to eliminate the fractions:
x(x+9) * (2/x) + x(x+9) * (4/(x+9)) = x(x+9) * 9
Simplifying each term gives:
2(x+9) + 4x = 9x(x+9)
Expanding and combining like terms:
2x + 18 + 4x = 9x^2 + 81x
Combining like terms again:
6x + 18 = 9x^2 + 81x
Now, we can rewrite the equation in standard form:
9x^2 + 75x - 18 = 0
From here, you can use the quadratic formula or factorization techniques to solve for x.