6x+2/3x+3 division sign 2x-2/4x+4
To simplify the expression (6x + 2)/(3x + 3) ÷ (2x - 2)/(4x + 4), you can follow these steps:
Step 1: Simplify each fraction individually.
The first fraction, (6x + 2)/(3x + 3), simplifies to (2(3x + 1))/(3(x + 1)).
The second fraction, (2x - 2)/(4x + 4), simplifies to (2(x - 1))/(4(x + 1)).
Step 2: Write the division as multiplication by the reciprocal.
The division sign (÷) can be changed to a multiplication sign (*) by taking the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator.
Flipping the second fraction, (2(x - 1))/(4(x + 1)), gives (4(x + 1))/(2(x - 1)).
Step 3: Multiply the fractions.
Now that we have the two fractions (2(3x + 1))/(3(x + 1)) and (4(x + 1))/(2(x - 1)), we can multiply them. To multiply fractions, we simply multiply the numerators together and the denominators together.
Multiplying the numerators, we get 2 * 4 * (3x + 1) * (x + 1), which simplifies to 8(3x + 1)(x + 1).
Multiplying the denominators, we get 3 * 2 * (x + 1) * (x - 1), which simplifies to 6(x + 1)(x - 1).
Step 4: Simplify the resulting fraction.
The resulting fraction after simplifying is 8(3x + 1)(x + 1) / 6(x + 1)(x - 1).
Step 5: Further simplification (if possible).
You can check if any factors can be canceled out. In this case, you can divide both the numerator and the denominator by their greatest common factor, which is 2.
Dividing both the numerator and the denominator by 2, we get 4(3x + 1)(x + 1) / 3(x + 1)(x - 1).
Thus, the simplified expression is 4(3x + 1)(x + 1) / 3(x + 1)(x - 1).