a 1 degree equation
-4 over 2x+3 + 1 over x-1 equals
1 over (2x+3)(x-1)
x=3
try writing it without the words. This is a math problem, not an English essay ...
-4/(2x+3) + 1/(x-1) = 1/((2x+3)(x-1))
-4(x-1) + 1(2x+3) = 1
-4x+4 + 2x+3 = 1
-2x+7 = 1
2x = 6
x = 3
To solve the equation (-4/(2x+3)) + (1/(x-1)) = 1/((2x+3)(x-1)), we need to find the value of 'x' that satisfies the equation. Let's break down the equation step by step:
Step 1: Clear the denominators
We can do this by multiplying every term in the equation by the common denominator, which is (2x+3)(x-1). By doing this, we eliminate the fractions in the equation:
(-4/(2x+3))(2x+3)(x-1) + (1/(x-1))(2x+3)(x-1) = (1/((2x+3)(x-1)))(2x+3)(x-1)
Step 2: Simplify the equation
When we multiply the fractions by their respective denominators, the denominators cancel out:
-4(x-1) + 1(2x+3) = 1
Step 3: Expand and simplify
Let's expand the brackets and simplify the equation further:
-4x + 4 + 2x + 3 = 1
-2x + 7 = 1
Step 4: Isolate the variable
To solve for 'x', we need to isolate the variable. Let's move the constant term to the right side of the equation:
-2x = 1 - 7
-2x = -6
Divide both sides by -2 to solve for 'x':
x = (-6)/(-2)
x = 3
Therefore, the solution to the equation (-4/(2x+3)) + (1/(x-1)) = (1/((2x+3)(x-1))) is x = 3.