3/t-3=5/t+4
3(t+4)(t-3)(5)
check this problem
To check the equation 3/(t-3) = 5/(t+4), we can start by cross-multiplying.
Cross-multiplying means multiplying the numerator of one fraction by the denominator of the other fraction.
For this equation, we multiply 3 by (t+4) and multiply 5 by (t-3).
On the left side of the equation, we get: 3(t+4).
On the right side of the equation, we get: 5(t-3).
Now, we can simplify both sides of the equation.
Expanding the equation, we get:
3(t+4) = 5(t-3)
3t + 12 = 5t - 15
Next, we need to isolate the variable t on one side of the equation.
Subtract 3t from both sides: 12 = 2t - 15
Add 15 to both sides: 27 = 2t
Finally, divide both sides by 2: t = 27/2
So, the solution to the original equation 3/(t-3) = 5/(t+4) is t = 27/2.
To check your problem: 3(t+4)(t-3)(5), we can simplify it.
We can start by multiplying the expression inside the parentheses: (t+4)(t-3).
Using the distributive property, we get: t(t) + t(-3) + 4(t) + 4(-3)
Simplifying further, we get: t^2 - 3t + 4t - 12
Combining like terms, we get: t^2 + t - 12
Now, we multiply the result by 3 and 5: 3(t^2 + t - 12)(5).
Using the distributive property again, we get: 3(t^2)(5) + 3(t)(5) + 3(-12)(5)
Simplifying further, we get: 15t^2 + 15t - 180
Therefore, the simplified expression 3(t+4)(t-3)(5) is equal to 15t^2 + 15t - 180.
Now that we have checked the problem, we can conclude that the equation 3/(t-3) = 5/(t+4) is valid and the expression 3(t+4)(t-3)(5) simplifies to 15t^2 + 15t - 180.