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受欢迎的代数 >

展开 (-16/5)/(t+3)+(11/5)/(t-2)

解答

展开

\frac{- \frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

解答

- \frac{t - 13}{t ^{2} + t - 6}

求解步骤

\frac{- \frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

\frac{- \frac{16}{5}}{t + 3} = - \frac{16}{5 t + 15}

= - \frac{16}{5 t + 15} + \frac{\frac{11}{5}}{t - 2}

\frac{\frac{11}{5}}{t - 2} = \frac{11}{5 t - 10}

= - \frac{16}{5 t + 15} + \frac{11}{5 t - 10}

分解

5 t + 15 : 5 (t + 3)

= - \frac{16}{5 ( t + 3 )} + \frac{11}{5 t - 10}

分解

5 t - 10 : 5 (t - 2)

= - \frac{16}{5 ( t + 3 )} + \frac{11}{5 ( t - 2 )}

5 (t + 3), 5 (t - 2)

的最小公倍数:

5 (t + 3) (t - 2)

根据最小公倍数调整分式

= - \frac{16 ( t - 2 )}{5 ( t + 3 ) ( t - 2 )} + \frac{11 ( t + 3 )}{5 ( t - 2 ) ( t + 3 )}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 16 ( t - 2 ) + 11 ( t + 3 )}{5 ( t + 3 ) ( t - 2 )}

分解

11 (t + 3) - 16 (t - 2) : - 5 (t - 13)

= - \frac{5 ( t - 13 )}{5 ( t + 3 ) ( t - 2 )}

数字相除:

\frac{5}{5} = 1

= - \frac{t - 13}{( t + 3 ) ( t - 2 )}

乘开

(t + 3) (t - 2) : t^{2} + t - 6

= - \frac{t - 13}{t ^{2} + t - 6}

流行的例子

展开 (2d+e+5t)(e+3t)

e x p an d (2 d + e + 5 t) (e + 3 t)

展开 (a^3+b^3+c^3)/((a+b)(a+c)(b+c))

e x p an d \frac{a ^{3} + b ^{3} + c ^{3}}{( a + b ) ( a + c ) ( b + c )}

展开 ((p-1))/(p^2(p^2-2p+5))

e x p an d \frac{( p - 1 )}{p ^{2} ( p ^{2} - 2 p + 5 )}

展开 ((y+1)^2)/y

e x p an d \frac{( y + 1 ) ^{2}}{y}

展开 (x-9)/((x-4)(x+4))

e x p an d \frac{x - 9}{( x - 4 ) ( x + 4 )}