Leysa x-1/x^2+4x+3+2/x^2+5x+6

$$\frac { x - 1 } { x ^ { 2 } + 4 x + 3 } + \frac { 2 } { x ^ { 2 } + 5 x + 6 }$$

Meta

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Skref að einfaldri lausn

Stuðull x^{2}+4x+3. Stuðull x^{2}+5x+6.

$$\frac{x-1}{\left(x+1\right)\left(x+3\right)}+\frac{2}{\left(x+2\right)\left(x+3\right)}$$

Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi \left(x+1\right)\left(x+3\right) og \left(x+2\right)\left(x+3\right) er \left(x+1\right)\left(x+2\right)\left(x+3\right). Margfaldaðu \frac{x-1}{\left(x+1\right)\left(x+3\right)} sinnum \frac{x+2}{x+2}. Margfaldaðu \frac{2}{\left(x+2\right)\left(x+3\right)} sinnum \frac{x+1}{x+1}.

$$\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\frac{2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Þar sem \frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} og \frac{2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.

$$\frac{\left(x-1\right)\left(x+2\right)+2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Margfaldaðu í \left(x-1\right)\left(x+2\right)+2\left(x+1\right).

$$\frac{x^{2}+2x-x-2+2x+2}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Sameinaðu svipaða liði í x^{2}+2x-x-2+2x+2.

$$\frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Þættaðu segðir sem hafa ekki þegar verið þættaðar í \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

$$\frac{x\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Styttu burt x+3 í bæði teljara og samnefnara.

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Víkka \left(x+1\right)\left(x+2\right).

$$\frac{x}{x^{2}+3x+2}$$

Víkka

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Skref að einfaldri lausn

Stuðull x^{2}+4x+3. Stuðull x^{2}+5x+6.

$$\frac{x-1}{\left(x+1\right)\left(x+3\right)}+\frac{2}{\left(x+2\right)\left(x+3\right)}$$

Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi \left(x+1\right)\left(x+3\right) og \left(x+2\right)\left(x+3\right) er \left(x+1\right)\left(x+2\right)\left(x+3\right). Margfaldaðu \frac{x-1}{\left(x+1\right)\left(x+3\right)} sinnum \frac{x+2}{x+2}. Margfaldaðu \frac{2}{\left(x+2\right)\left(x+3\right)} sinnum \frac{x+1}{x+1}.

$$\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\frac{2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Þar sem \frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} og \frac{2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.

$$\frac{\left(x-1\right)\left(x+2\right)+2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Margfaldaðu í \left(x-1\right)\left(x+2\right)+2\left(x+1\right).

$$\frac{x^{2}+2x-x-2+2x+2}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Sameinaðu svipaða liði í x^{2}+2x-x-2+2x+2.

$$\frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Þættaðu segðir sem hafa ekki þegar verið þættaðar í \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

$$\frac{x\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Styttu burt x+3 í bæði teljara og samnefnara.

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Víkka \left(x+1\right)\left(x+2\right).

$$\frac{x}{x^{2}+3x+2}$$