(frac{a^{2}}{a+B}-frac{a^{3}}{a^{2}+2aB+B^2}):(a/a+B-a^2/a^2-B^2) eching

$$( \frac { a ^ { 2 } } { a + B } - \frac { a ^ { 3 } } { a ^ { 2 } + 2 a B + B ^ { 2 } } ) : ( \frac { a } { a + B } - \frac { a ^ { 2 } } { a ^ { 2 } - B ^ { 2 } } )$$

Baholash

$$-\frac{a\left(a-B\right)}{B+a}$$

Qisqa yechim qadamlari

Faktor: a^{2}+2aB+B^{2}.

$$\frac{\frac{a^{2}}{a+B}-\frac{a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a+B va \left(B+a\right)^{2} ning eng kichik umumiy karralisi \left(B+a\right)^{2}. \frac{a^{2}}{a+B} ni \frac{B+a}{B+a} marotabaga ko'paytirish.

$$\frac{\frac{a^{2}\left(B+a\right)}{\left(B+a\right)^{2}}-\frac{a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

\frac{a^{2}\left(B+a\right)}{\left(B+a\right)^{2}} va \frac{a^{3}}{\left(B+a\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{a^{2}\left(B+a\right)-a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

a^{2}\left(B+a\right)-a^{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{a^{2}B+a^{3}-a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

a^{2}B+a^{3}-a^{3} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

Faktor: a^{2}-B^{2}.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a+B va \left(B+a\right)\left(-B+a\right) ning eng kichik umumiy karralisi \left(B+a\right)\left(-B+a\right). \frac{a}{a+B} ni \frac{-B+a}{-B+a} marotabaga ko'paytirish.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a\left(-B+a\right)}{\left(B+a\right)\left(-B+a\right)}-\frac{a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

\frac{a\left(-B+a\right)}{\left(B+a\right)\left(-B+a\right)} va \frac{a^{2}}{\left(B+a\right)\left(-B+a\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a\left(-B+a\right)-a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

a\left(-B+a\right)-a^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{-aB+a^{2}-a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

-aB+a^{2}-a^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{-aB}{\left(B+a\right)\left(-B+a\right)}}$$

\frac{a^{2}B}{\left(B+a\right)^{2}} ni \frac{-aB}{\left(B+a\right)\left(-B+a\right)} ga bo'lish \frac{a^{2}B}{\left(B+a\right)^{2}} ga k'paytirish \frac{-aB}{\left(B+a\right)\left(-B+a\right)} ga qaytarish.

$$\frac{a^{2}B\left(B+a\right)\left(-B+a\right)}{\left(B+a\right)^{2}\left(-1\right)aB}$$

Surat va maxrajdagi ikkala Ba\left(B+a\right) ni qisqartiring.

$$\frac{a\left(-B+a\right)}{-\left(B+a\right)}$$

a ga -B+a ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{-aB+a^{2}}{-\left(B+a\right)}$$

B+a teskarisini topish uchun har birining teskarisini toping.

$$\frac{-aB+a^{2}}{-B-a}$$

Kengaytirish

$$-\frac{a^{2}-Ba}{B+a}$$

Qisqa yechim qadamlari

Faktor: a^{2}+2aB+B^{2}.

$$\frac{\frac{a^{2}}{a+B}-\frac{a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a+B va \left(B+a\right)^{2} ning eng kichik umumiy karralisi \left(B+a\right)^{2}. \frac{a^{2}}{a+B} ni \frac{B+a}{B+a} marotabaga ko'paytirish.

$$\frac{\frac{a^{2}\left(B+a\right)}{\left(B+a\right)^{2}}-\frac{a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

\frac{a^{2}\left(B+a\right)}{\left(B+a\right)^{2}} va \frac{a^{3}}{\left(B+a\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{a^{2}\left(B+a\right)-a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

a^{2}\left(B+a\right)-a^{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{a^{2}B+a^{3}-a^{3}}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

a^{2}B+a^{3}-a^{3} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{a^{2}-B^{2}}}$$

Faktor: a^{2}-B^{2}.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a}{a+B}-\frac{a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a+B va \left(B+a\right)\left(-B+a\right) ning eng kichik umumiy karralisi \left(B+a\right)\left(-B+a\right). \frac{a}{a+B} ni \frac{-B+a}{-B+a} marotabaga ko'paytirish.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a\left(-B+a\right)}{\left(B+a\right)\left(-B+a\right)}-\frac{a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

\frac{a\left(-B+a\right)}{\left(B+a\right)\left(-B+a\right)} va \frac{a^{2}}{\left(B+a\right)\left(-B+a\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{a\left(-B+a\right)-a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

a\left(-B+a\right)-a^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{-aB+a^{2}-a^{2}}{\left(B+a\right)\left(-B+a\right)}}$$

-aB+a^{2}-a^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{a^{2}B}{\left(B+a\right)^{2}}}{\frac{-aB}{\left(B+a\right)\left(-B+a\right)}}$$

\frac{a^{2}B}{\left(B+a\right)^{2}} ni \frac{-aB}{\left(B+a\right)\left(-B+a\right)} ga bo'lish \frac{a^{2}B}{\left(B+a\right)^{2}} ga k'paytirish \frac{-aB}{\left(B+a\right)\left(-B+a\right)} ga qaytarish.

$$\frac{a^{2}B\left(B+a\right)\left(-B+a\right)}{\left(B+a\right)^{2}\left(-1\right)aB}$$

Surat va maxrajdagi ikkala Ba\left(B+a\right) ni qisqartiring.

$$\frac{a\left(-B+a\right)}{-\left(B+a\right)}$$

a ga -B+a ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{-aB+a^{2}}{-\left(B+a\right)}$$

B+a teskarisini topish uchun har birining teskarisini toping.

$$\frac{-aB+a^{2}}{-B-a}$$