Solve (x^2+4x+3)x^-1/2

$$( x ^ { 2 } + 4 x + 3 ) x ^ { - 1 / 2 }$$

Evaluate

$$\frac{\left(x+1\right)\left(x+3\right)}{\sqrt{x}}$$

Solution Steps

Use the distributive property to multiply x^{2}+4x+3 by x^{-\frac{1}{2}}.

$$x^{2}x^{-\frac{1}{2}}+4xx^{-\frac{1}{2}}+3x^{-\frac{1}{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and -\frac{1}{2} to get \frac{3}{2}.

$$x^{\frac{3}{2}}+4xx^{-\frac{1}{2}}+3x^{-\frac{1}{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -\frac{1}{2} to get \frac{1}{2}.

$$x^{\frac{3}{2}}+4x^{\frac{1}{2}}+3x^{-\frac{1}{2}}$$

Factor

$$\frac{\left(x+1\right)\left(x+3\right)}{\sqrt{x}}$$