Problem 6
Question
Simplify the expression. $$\frac{3 x}{x^{2}-2 x-15} \cdot(x+3)$$
Step-by-Step Solution
Verified Answer
The simplified expression is \(3x(x-5)\)
1Step 1: Factorization of the quadratic expression
The quadratic expression \(x^{2}-2 x-15\) in the denominator can be factored into \((x-5)(x+3)\). Therefore the expression becomes: \(\frac{3 x}{(x-5)(x+3)} * (x+3)\)
2Step 2: Cancellation of common factors
Notice that \((x+3)\) is present in both the numerator and the denominator. Hence, they cancel each other. The simplified expression is: \(\frac{3 x}{x-5}\).
3Step 3: Verification and expansion
We have crossed cancelled and the expression is much simpler. We can multiply out the numerator \(3x\) by the denominator \((x-5)\). Thus, the final expression is: \(3x(x-5)\)
Other exercises in this chapter
Problem 6
Solve the equation using the cross product property. Remember to check your solutions. \(\frac{3}{x}=\frac{x}{12}\)
View solution Problem 6
Solve the proportion. Check your solution. $$ \frac{2}{2 x+1}=\frac{1}{5} $$
View solution Problem 6
Simplify the expression. If not possible, write already in simplest form. $$ \frac{12 x^{2}}{6 x} $$
View solution Problem 7
Does the equation model direct variation, inverse variation, or neither? $$ y=7 x-2 $$
View solution