Final answer:
To solve the equation (4)/(7)+(3)/(x-3)=(53)/(56), find a common denominator, distribute and simplify the equation, combine like terms, subtract and add terms to isolate x, and divide to solve for x.
Step-by-step explanation:
To solve the equation (4)/(7)+(3)/(x-3)=(53)/(56), we can start by getting rid of the denominators by finding a common denominator. In this case, the common denominator is 56(x-3). Multiplying every term in the equation by 56(x-3), we get 4(x-3) + 56(3) = 53(x-3).
Now, distribute and simplify the equation: 4x - 12 + 168 = 53x - 159.
Combine like terms: 4x + 156 = 53x - 159.
Subtract 4x from both sides: 156 = 49x - 159.
Add 159 to both sides: 315 = 49x.
Finally, divide both sides by 49 to solve for x: x = 315/49.