Evaluasi
\frac{9x\left(x+1\right)}{8}
Luaskan
\frac{9x^{2}+9x}{8}
Grafik
Bagikan
Disalin ke clipboard
\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari x+1 dan x-2 adalah \left(x-2\right)\left(x+1\right). Kalikan \frac{x-2}{x+1} kali \frac{x-2}{x-2}. Kalikan \frac{5-x}{x-2} kali \frac{x+1}{x+1}.
\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Karena \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} dan \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} memiliki penyebut yang sama, tambahkan bilangan dengan menambahkan pembilangnya.
\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Kalikan bilangan berikut \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Gabungkan seperti suku di x^{2}-2x-2x+4+5x+5-x^{2}-x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Faktor dari x^{2}-x-2. Faktor dari x^{2}+3x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari \left(x-2\right)\left(x+1\right) dan \left(x+1\right)\left(x+2\right) adalah \left(x-2\right)\left(x+1\right)\left(x+2\right). Kalikan \frac{1}{\left(x-2\right)\left(x+1\right)} kali \frac{x+2}{x+2}. Kalikan \frac{1}{\left(x+1\right)\left(x+2\right)} kali \frac{x-2}{x-2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Karena \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} dan \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Kalikan bilangan berikut x+2-\left(x-2\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Gabungkan seperti suku di x+2-x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Faktor dari x^{2}+x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari x dan x\left(x+1\right) adalah x\left(x+1\right). Kalikan \frac{x+1}{x} kali \frac{x+1}{x+1}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}
Karena \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} dan \frac{3-x^{2}}{x\left(x+1\right)} memiliki penyebut yang sama, tambahkan bilangan dengan menambahkan pembilangnya.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}
Kalikan bilangan berikut \left(x+1\right)\left(x+1\right)+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}
Gabungkan seperti suku di x^{2}+x+1+x+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}
Kalikan \frac{2x+4}{x\left(x+1\right)} dan \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} dengan mengalikan bilangan pembilang dengan pembilang serta penyebut dengan penyebut.
\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}
Bagi \frac{9}{\left(x-2\right)\left(x+1\right)} dengan \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} dengan mengalikan \frac{9}{\left(x-2\right)\left(x+1\right)} sesuai dengan resiprokal dari \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}.
\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}
Sederhanakan \left(x-2\right)\left(x+1\right) di pembilang dan penyebut.
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
Faktorkan ekspresi yang belum difaktorkan.
\frac{9x\left(x+1\right)}{2\times 4}
Sederhanakan x+2 di pembilang dan penyebut.
\frac{9x^{2}+9x}{8}
Perluas ekspresi.
\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari x+1 dan x-2 adalah \left(x-2\right)\left(x+1\right). Kalikan \frac{x-2}{x+1} kali \frac{x-2}{x-2}. Kalikan \frac{5-x}{x-2} kali \frac{x+1}{x+1}.
\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Karena \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} dan \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} memiliki penyebut yang sama, tambahkan bilangan dengan menambahkan pembilangnya.
\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Kalikan bilangan berikut \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Gabungkan seperti suku di x^{2}-2x-2x+4+5x+5-x^{2}-x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Faktor dari x^{2}-x-2. Faktor dari x^{2}+3x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari \left(x-2\right)\left(x+1\right) dan \left(x+1\right)\left(x+2\right) adalah \left(x-2\right)\left(x+1\right)\left(x+2\right). Kalikan \frac{1}{\left(x-2\right)\left(x+1\right)} kali \frac{x+2}{x+2}. Kalikan \frac{1}{\left(x+1\right)\left(x+2\right)} kali \frac{x-2}{x-2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Karena \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} dan \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Kalikan bilangan berikut x+2-\left(x-2\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Gabungkan seperti suku di x+2-x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Faktor dari x^{2}+x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari x dan x\left(x+1\right) adalah x\left(x+1\right). Kalikan \frac{x+1}{x} kali \frac{x+1}{x+1}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}
Karena \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} dan \frac{3-x^{2}}{x\left(x+1\right)} memiliki penyebut yang sama, tambahkan bilangan dengan menambahkan pembilangnya.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}
Kalikan bilangan berikut \left(x+1\right)\left(x+1\right)+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}
Gabungkan seperti suku di x^{2}+x+1+x+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}
Kalikan \frac{2x+4}{x\left(x+1\right)} dan \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} dengan mengalikan bilangan pembilang dengan pembilang serta penyebut dengan penyebut.
\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}
Bagi \frac{9}{\left(x-2\right)\left(x+1\right)} dengan \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} dengan mengalikan \frac{9}{\left(x-2\right)\left(x+1\right)} sesuai dengan resiprokal dari \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}.
\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}
Sederhanakan \left(x-2\right)\left(x+1\right) di pembilang dan penyebut.
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
Faktorkan ekspresi yang belum difaktorkan.
\frac{9x\left(x+1\right)}{2\times 4}
Sederhanakan x+2 di pembilang dan penyebut.
\frac{9x^{2}+9x}{8}
Perluas ekspresi.
Contoh
Persamaan kuadrat
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometri
4 \sin \theta \cos \theta = 2 \sin \theta
Persamaan linear
y = 3x + 4
Aritmetika
699 * 533
Matriks
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Persamaan simultan
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Diferensial
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integral
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limit
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}