Lahenda 4(1/x+9-1/x)+4(1/x+9-1/x)+4x(frac{-1}{(x+9)^2}+frac{1}{x^2})

$$4 ( \frac { 1 } { x + 9 } - \frac { 1 } { x } ) + 4 ( \frac { 1 } { x + 9 } - \frac { 1 } { x } ) + 4 x ( \frac { - 1 } { ( x + 9 ) ^ { 2 } } + \frac { 1 } { x ^ { 2 } } )$$

Arvuta

$$-\frac{324}{x\left(x+9\right)^{2}}$$

Lühike lahenduskäik

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. x+9 ja x vähim ühiskordne on x\left(x+9\right). Korrutage omavahel \frac{1}{x+9} ja \frac{x}{x}. Korrutage omavahel \frac{1}{x} ja \frac{x+9}{x+9}.

$$4\left(\frac{x}{x\left(x+9\right)}-\frac{x+9}{x\left(x+9\right)}\right)+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kuna murdudel \frac{x}{x\left(x+9\right)} ja \frac{x+9}{x\left(x+9\right)} on sama nimetaja, lahutage nende lugejad.

$$4\times \frac{x-\left(x+9\right)}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Tehke korrutustehted võrrandis x-\left(x+9\right).

$$4\times \frac{x-x-9}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kombineerige sarnased liikmed avaldises x-x-9.

$$4\times \frac{-9}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldage 4\times \frac{-9}{x\left(x+9\right)} ühe murdarvuna.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. x+9 ja x vähim ühiskordne on x\left(x+9\right). Korrutage omavahel \frac{1}{x+9} ja \frac{x}{x}. Korrutage omavahel \frac{1}{x} ja \frac{x+9}{x+9}.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\left(\frac{x}{x\left(x+9\right)}-\frac{x+9}{x\left(x+9\right)}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kuna murdudel \frac{x}{x\left(x+9\right)} ja \frac{x+9}{x\left(x+9\right)} on sama nimetaja, lahutage nende lugejad.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\times \frac{x-\left(x+9\right)}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Tehke korrutustehted võrrandis x-\left(x+9\right).

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\times \frac{x-x-9}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kombineerige sarnased liikmed avaldises x-x-9.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\times \frac{-9}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldage 4\times \frac{-9}{x\left(x+9\right)} ühe murdarvuna.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(-9\right)}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kombineerige \frac{4\left(-9\right)}{x\left(x+9\right)} ja \frac{4\left(-9\right)}{x\left(x+9\right)}, et leida 2\times \frac{4\left(-9\right)}{x\left(x+9\right)}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x+9\right)^{2} ja x^{2} vähim ühiskordne on x^{2}\left(x+9\right)^{2}. Korrutage omavahel \frac{-1}{\left(x+9\right)^{2}} ja \frac{x^{2}}{x^{2}}. Korrutage omavahel \frac{1}{x^{2}} ja \frac{\left(x+9\right)^{2}}{\left(x+9\right)^{2}}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\left(\frac{-x^{2}}{x^{2}\left(x+9\right)^{2}}+\frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}}\right)$$

Kuna murdudel \frac{-x^{2}}{x^{2}\left(x+9\right)^{2}} ja \frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}} on sama nimetaja, liitke nende lugejad.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}}$$

Tehke korrutustehted võrrandis -x^{2}+\left(x+9\right)^{2}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+x^{2}+18x+81}{x^{2}\left(x+9\right)^{2}}$$

Kombineerige sarnased liikmed avaldises -x^{2}+x^{2}+18x+81.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}}$$

Avaldage 4\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}} ühe murdarvuna.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Korrutage 4 ja -9, et leida -36.

$$2\times \frac{-36}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Avaldage 2\times \frac{-36}{x\left(x+9\right)} ühe murdarvuna.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Kasutage distributiivsusomadust, et korrutada 4 ja 18x+81.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x$$

Avaldage \frac{72x+324}{x^{2}\left(x+9\right)^{2}}x ühe murdarvuna.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{\left(72x+324\right)x}{x^{2}\left(x+9\right)^{2}}$$

Taandage x nii lugejas kui ka nimetajas.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. x\left(x+9\right) ja x\left(x+9\right)^{2} vähim ühiskordne on x\left(x+9\right)^{2}. Korrutage omavahel \frac{2\left(-36\right)}{x\left(x+9\right)} ja \frac{x+9}{x+9}.

$$\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Kuna murdudel \frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} ja \frac{72x+324}{x\left(x+9\right)^{2}} on sama nimetaja, liitke nende lugejad.

$$\frac{2\left(-36\right)\left(x+9\right)+72x+324}{x\left(x+9\right)^{2}}$$

Tehke korrutustehted võrrandis 2\left(-36\right)\left(x+9\right)+72x+324.

$$\frac{-72x-648+72x+324}{x\left(x+9\right)^{2}}$$

Kombineerige sarnased liikmed avaldises -72x-648+72x+324.

$$\frac{-324}{x\left(x+9\right)^{2}}$$

Laiendage x\left(x+9\right)^{2}.

$$\frac{-324}{x^{3}+18x^{2}+81x}$$

Laienda

$$-\frac{324}{x\left(x+9\right)^{2}}$$

Lühike lahenduskäik

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. x+9 ja x vähim ühiskordne on x\left(x+9\right). Korrutage omavahel \frac{1}{x+9} ja \frac{x}{x}. Korrutage omavahel \frac{1}{x} ja \frac{x+9}{x+9}.

$$4\left(\frac{x}{x\left(x+9\right)}-\frac{x+9}{x\left(x+9\right)}\right)+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kuna murdudel \frac{x}{x\left(x+9\right)} ja \frac{x+9}{x\left(x+9\right)} on sama nimetaja, lahutage nende lugejad.

$$4\times \frac{x-\left(x+9\right)}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Tehke korrutustehted võrrandis x-\left(x+9\right).

$$4\times \frac{x-x-9}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kombineerige sarnased liikmed avaldises x-x-9.

$$4\times \frac{-9}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldage 4\times \frac{-9}{x\left(x+9\right)} ühe murdarvuna.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\left(\frac{1}{x+9}-\frac{1}{x}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. x+9 ja x vähim ühiskordne on x\left(x+9\right). Korrutage omavahel \frac{1}{x+9} ja \frac{x}{x}. Korrutage omavahel \frac{1}{x} ja \frac{x+9}{x+9}.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\left(\frac{x}{x\left(x+9\right)}-\frac{x+9}{x\left(x+9\right)}\right)+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kuna murdudel \frac{x}{x\left(x+9\right)} ja \frac{x+9}{x\left(x+9\right)} on sama nimetaja, lahutage nende lugejad.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\times \frac{x-\left(x+9\right)}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Tehke korrutustehted võrrandis x-\left(x+9\right).

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\times \frac{x-x-9}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kombineerige sarnased liikmed avaldises x-x-9.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+4\times \frac{-9}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldage 4\times \frac{-9}{x\left(x+9\right)} ühe murdarvuna.

$$\frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(-9\right)}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Kombineerige \frac{4\left(-9\right)}{x\left(x+9\right)} ja \frac{4\left(-9\right)}{x\left(x+9\right)}, et leida 2\times \frac{4\left(-9\right)}{x\left(x+9\right)}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\left(\frac{-1}{\left(x+9\right)^{2}}+\frac{1}{x^{2}}\right)$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x+9\right)^{2} ja x^{2} vähim ühiskordne on x^{2}\left(x+9\right)^{2}. Korrutage omavahel \frac{-1}{\left(x+9\right)^{2}} ja \frac{x^{2}}{x^{2}}. Korrutage omavahel \frac{1}{x^{2}} ja \frac{\left(x+9\right)^{2}}{\left(x+9\right)^{2}}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\left(\frac{-x^{2}}{x^{2}\left(x+9\right)^{2}}+\frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}}\right)$$

Kuna murdudel \frac{-x^{2}}{x^{2}\left(x+9\right)^{2}} ja \frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}} on sama nimetaja, liitke nende lugejad.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}}$$

Tehke korrutustehted võrrandis -x^{2}+\left(x+9\right)^{2}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+x^{2}+18x+81}{x^{2}\left(x+9\right)^{2}}$$

Kombineerige sarnased liikmed avaldises -x^{2}+x^{2}+18x+81.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}}$$

Avaldage 4\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}} ühe murdarvuna.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Korrutage 4 ja -9, et leida -36.

$$2\times \frac{-36}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Avaldage 2\times \frac{-36}{x\left(x+9\right)} ühe murdarvuna.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Kasutage distributiivsusomadust, et korrutada 4 ja 18x+81.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x$$

Avaldage \frac{72x+324}{x^{2}\left(x+9\right)^{2}}x ühe murdarvuna.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{\left(72x+324\right)x}{x^{2}\left(x+9\right)^{2}}$$

Taandage x nii lugejas kui ka nimetajas.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. x\left(x+9\right) ja x\left(x+9\right)^{2} vähim ühiskordne on x\left(x+9\right)^{2}. Korrutage omavahel \frac{2\left(-36\right)}{x\left(x+9\right)} ja \frac{x+9}{x+9}.

$$\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Kuna murdudel \frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} ja \frac{72x+324}{x\left(x+9\right)^{2}} on sama nimetaja, liitke nende lugejad.

$$\frac{2\left(-36\right)\left(x+9\right)+72x+324}{x\left(x+9\right)^{2}}$$

Tehke korrutustehted võrrandis 2\left(-36\right)\left(x+9\right)+72x+324.

$$\frac{-72x-648+72x+324}{x\left(x+9\right)^{2}}$$

Kombineerige sarnased liikmed avaldises -72x-648+72x+324.

$$\frac{-324}{x\left(x+9\right)^{2}}$$

Laiendage x\left(x+9\right)^{2}.

$$\frac{-324}{x^{3}+18x^{2}+81x}$$