Question:
Find the partial fractions for the following expression:
![](https://static.wixstatic.com/media/20c892_58aba17f322445b1a009f1eb64f30dda~mv2.png/v1/fill/w_980,h_87,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/20c892_58aba17f322445b1a009f1eb64f30dda~mv2.png)
Answer:
As powers are equal in both the numerator and denominator we must use polynomial division first to find the remainder.
![](https://static.wixstatic.com/media/20c892_1c1e1f114902416b90b3f24668e2d01c~mv2.png/v1/fill/w_980,h_110,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/20c892_1c1e1f114902416b90b3f24668e2d01c~mv2.png)
Now proceed to find partial fractions.
![](https://static.wixstatic.com/media/20c892_f85af84618144ab4bacab844f6a4274b~mv2.png/v1/fill/w_980,h_292,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/20c892_f85af84618144ab4bacab844f6a4274b~mv2.png)
Sub x = -2 into the equation to remove A from the variables:
![](https://static.wixstatic.com/media/20c892_cb6720d9ed654c6eba4663f70aeb41d0~mv2.png/v1/fill/w_980,h_149,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/20c892_cb6720d9ed654c6eba4663f70aeb41d0~mv2.png)
Sub x = 5 into the equation to remove B from the variables:
![](https://static.wixstatic.com/media/20c892_0c69f7e8833c4ab193e7bf15713e00ff~mv2.png/v1/fill/w_980,h_261,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/20c892_0c69f7e8833c4ab193e7bf15713e00ff~mv2.png)
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