The equivalent expression of 4 / (p² + 7p + 12) is 4 / (p + 3)(p + 4).
The equivalent expression of 3p / (p² + 8p + 15) is 3p/ (p + 3)(p + 5).
How to rewrite the expression?
The given expression is rewritten as an equivalent rational expression using the LCD as follows;
The given expression;
4 / (p² + 7p + 12)
The denominator is factorized as follows;
= p² + 7p + 12
= p² + 4p + 3p + 12
= p(p + 4) + 3(p + 4)
= (p + 3)(p + 4)
The LCD = (p + 3)(p + 4)
The equivalent expression = 4 / (p + 3)(p + 4)
The given expression;
3p / (p² + 8p + 15)
The factorize;
= p² + 8p + 15
= p² + 3p + 5p + 15
= p(p + 3) + 5(p + 3)
= (p + 3)(p + 5)
The equivalent expression = 3p/ (p + 3)(p + 5)