Løs 9/w^2-w-12+w/w^2+8w+15

$$\frac { 9 } { w ^ { 2 } - w - 12 } + \frac { w } { w ^ { 2 } + 8 w + 15 }$$

Evaluer

$$\frac{w^{2}+5w+45}{\left(w-4\right)\left(w+3\right)\left(w+5\right)}$$

Korte løsningstrin

Faktoriser w^{2}-w-12. Faktoriser w^{2}+8w+15.

$$\frac{9}{\left(w-4\right)\left(w+3\right)}+\frac{w}{\left(w+3\right)\left(w+5\right)}$$

For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for \left(w-4\right)\left(w+3\right) og \left(w+3\right)\left(w+5\right) er \left(w-4\right)\left(w+3\right)\left(w+5\right). Multiplicer \frac{9}{\left(w-4\right)\left(w+3\right)} gange \frac{w+5}{w+5}. Multiplicer \frac{w}{\left(w+3\right)\left(w+5\right)} gange \frac{w-4}{w-4}.

$$\frac{9\left(w+5\right)}{\left(w-4\right)\left(w+3\right)\left(w+5\right)}+\frac{w\left(w-4\right)}{\left(w-4\right)\left(w+3\right)\left(w+5\right)}$$

Da \frac{9\left(w+5\right)}{\left(w-4\right)\left(w+3\right)\left(w+5\right)} og \frac{w\left(w-4\right)}{\left(w-4\right)\left(w+3\right)\left(w+5\right)} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.

$$\frac{9\left(w+5\right)+w\left(w-4\right)}{\left(w-4\right)\left(w+3\right)\left(w+5\right)}$$

Lav multiplikationerne i 9\left(w+5\right)+w\left(w-4\right).

$$\frac{9w+45+w^{2}-4w}{\left(w-4\right)\left(w+3\right)\left(w+5\right)}$$

Kombiner ens led i 9w+45+w^{2}-4w.

$$\frac{5w+45+w^{2}}{\left(w-4\right)\left(w+3\right)\left(w+5\right)}$$

Udvid \left(w-4\right)\left(w+3\right)\left(w+5\right).

$$\frac{5w+45+w^{2}}{w^{3}+4w^{2}-17w-60}$$

Differentier w.r.t. w

$$\frac{465-480w-172w^{2}-10w^{3}-w^{4}}{\left(\left(w-4\right)\left(w+3\right)\left(w+5\right)\right)^{2}}$$