Simplify into on fraction.
(-5x/x+3)-(7/x+3)
• (-5x-7)/(x+3)
• (-5x+7)/(x+3)
• (-5x-7)/(x+3)^3
• (-5x+7)/(x+3)^2
How?
(-5x/x+3)-(7/x+3)
(-5x-7)/(x+3)
To simplify the given expression into one fraction, you need to combine the two fractions using a common denominator.
The expression is (-5x/(x+3)) - (7/(x+3)).
Step 1: Find the common denominator.
The denominators in the two fractions are both (x+3), so this will be our common denominator.
Step 2: Convert each fraction so that its denominator is the common denominator.
For the first fraction, multiply both the numerator and denominator by (x+3):
((-5x * (x+3))/((x+3)*(x+3)))
= (-5x(x+3))/((x+3)^2)
For the second fraction, the denominator is already (x+3), so there is no need for conversion.
Step 3: Combine the fractions by subtracting them.
(-5x(x+3))/((x+3)^2) - (7/(x+3))
Step 4: Simplify the combined fraction.
To subtract the fractions, you need to subtract the numerators while keeping the common denominator:
= (-5x(x+3) - 7)/((x+3)^2)
= (-5x^2 - 15x - 7)/((x+3)^2)
So, the simplified expression is (-5x^2 - 15x - 7)/((x+3)^2).
Therefore, the correct option is (-5x^2 - 15x - 7)/((x+3)^2).