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8.3E: Mazoezi

  • Page ID
    177724
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    Mazoezi hufanya kamili

    Ongeza Maneno ya busara na Denominator ya kawaida

    Katika mazoezi yafuatayo, ongeza.

    Mfano\(\PageIndex{25}\)

    \(\frac{2}{15}+\frac{7}{15}\)

    Jibu

    \(\frac{3}{5}\)

    Mfano\(\PageIndex{26}\)

    \(\frac{4}{21}+\frac{3}{21}\)

    Mfano\(\PageIndex{27}\)

    \(\frac{7}{24}+\frac{11}{24}\)

    Jibu

    \(\frac{3}{4}\)

    Mfano\(\PageIndex{28}\)

    \(\frac{7}{36}+\frac{13}{36}\)

    Mfano\(\PageIndex{29}\)

    \(\frac{3a}{a−b}+\frac{1}{a−b}\)

    Jibu

    \(\frac{3a+1}{a-b}\)

    Mfano\(\PageIndex{30}\)

    \(\frac{3c}{4c−5}+\frac{5}{4c−5}\)

    Mfano\(\PageIndex{31}\)

    \(\frac{d}{d+8}+\frac{5}{d+8}\)

    Jibu

    \(\frac{d+5}{d+8}\)

    Mfano\(\PageIndex{32}\)

    \(\frac{7m}{2m+n}+\frac{4}{2m+n}\)

    Mfano\(\PageIndex{33}\)

    \(\frac{p^2+10p}{p+2}+\frac{16}{p+2}\)

    Jibu

    p+8

    Mfano\(\PageIndex{34}\)

    \(\frac{q^2+12q}{q+3}+\frac{27}{q+3}\)

    Mfano\(\PageIndex{35}\)

    \(\frac{2r^2}{2r−1}+\frac{15r−8}{2r−1}\)

    Jibu

    r+8

    Mfano\(\PageIndex{36}\)

    \(\frac{3s^2}{3s−2}+\frac{13s−10}{3s−2}\)

    Mfano\(\PageIndex{37}\)

    \(\frac{8t^2}{t+4}+\frac{32t}{t+4}\)

    Jibu

    8t

    Mfano\(\PageIndex{38}\)

    \(\frac{6v^2}{v+5}+\frac{30v}{v+5}\)

    Mfano\(\PageIndex{39}\)

    \(\frac{2w^2}{w^2−16}+\frac{8w}{w^2−16}\)

    Jibu

    \(\frac{2w}{w−4}\)

    Mfano\(\PageIndex{40}\)

    \(\frac{7x^2}{x^2−9}+\frac{21x}{x^2−9}\)

    Ondoa Maneno ya busara na Denominator ya kawaida

    Katika mazoezi yafuatayo, toa.

    Mfano\(\PageIndex{41}\)

    \(\frac{y^2}{y+8}−\frac{64}{y+8}\)

    Jibu

    y-8

    Mfano\(\PageIndex{42}\)

    \(\frac{z^2}{z+2}−\frac{4}{z+2}\)

    Mfano\(\PageIndex{43}\)

    \(\frac{9a^2}{3a−7}−\frac{49}{3a−7}\)

    Jibu

    3a+7

    Mfano\(\PageIndex{44}\)

    \(\frac{25b^2}{5b−6}−\frac{36}{5b−6}\)

    Mfano\(\PageIndex{45}\)

    \(\frac{c^2}{c−8}−\frac{6c+16}{c−8}\)

    Jibu

    c+2

    Mfano\(\PageIndex{46}\)

    \(\frac{d^2}{d−9}−\frac{6d+27}{d−9}\)

    Mfano\(\PageIndex{47}\)

    \(\frac{3m^2}{6m−30}−\frac{21m−30}{6m−30}\)

    Jibu

    \(\frac{m−2}{3}\)

    Mfano\(\PageIndex{48}\)

    \(\frac{2n^2}{4n−32}−\frac{30n−16}{4n−32}\)

    Mfano\(\PageIndex{49}\)

    \(\frac{6p^2+3p+4}{p^2+4p−5}−\frac{5p^2+p+7}{p^2+4p−5}\)

    Jibu

    \(\frac{p+3}{p+5}\)

    Mfano\(\PageIndex{50}\)

    \(\frac{5q^2+3q−9}{q^2+6q+8}−\frac{4q^2+9q+7}{q^2+6q+8}\)

    Mfano\(\PageIndex{51}\)

    \(\frac{5r^2+7r−33}{r^2−49}−\frac{4r^2−5r−30}{r^2−49}\)

    Jibu

    \(\frac{r+9}{r+7}\)

    Mfano\(\PageIndex{52}\)

    \(\frac{7t^2−t−4}{t^2−25}−\frac{6t^2+2t−1}{t^2−25}\)

    Ongeza na Ondoa Maneno ya Mantiki ambao Denominators ni kinyume

    Katika mazoezi yafuatayo, ongeza.

    Mfano\(\PageIndex{53}\)

    \(\frac{10v^2}{v−1}+\frac{2v+4}{1−2v}\)

    Jibu

    4

    Mfano\(\PageIndex{54}\)

    \(\frac{20w}{5w−2}+\frac{5w+6}{2−5w}\)

    Mfano\(\PageIndex{55}\)

    \(\frac{10x^2+16x−7}{8x−3}+\frac{2x^2+3x−1}{3−8x}\)

    Jibu

    x+2

    Mfano\(\PageIndex{56}\)

    \(\frac{6y^2+2y−11}{3y−7}+\frac{3y^2−3y+17}{7−3y}\)

    Katika mazoezi yafuatayo, toa.

    Mfano\(\PageIndex{57}\)

    \(\frac{z^2+6z}{z^2−25}−\frac{3z+20}{25−z^2}\)

    Jibu

    \(\frac{z+4}{z−5}\)

    Mfano\(\PageIndex{58}\)

    \(\frac{a^2+3a}{a^2−9}−\frac{3a−27}{9−a^2}\)

    Mfano\(\PageIndex{59}\)

    \(\frac{2b^2+30b−13}{b^2−49}−\frac{2b^2−5b−8}{49−b^2}\)

    Jibu

    \(\frac{4b−3}{b−7}\)

    Mfano\(\PageIndex{60}\)

    \(\frac{c^2+5c−10}{c^2−16}−\frac{c^2−8c−10}{16−c^2}\)

    kila siku Math

    Mfano\(\PageIndex{61}\)

    Sarah mbio 8 maili na kisha baiskeli 24 maili. Biking kasi yake ni 4 mph kasi zaidi kuliko kasi yake mbio. Ikiwa rr inawakilisha kasi ya Sarah wakati yeye mbio, basi muda wake wa kukimbia unatokana\(\frac{8}{r}\) na usemi na wakati wake wa kuendesha baiskeli unatokana na maneno\(\frac{24}{r+4}\). Kuongeza maneno mantiki ya kupata\(\frac{8}{r}+\frac{24}{r+4}\) kujieleza kwa jumla ya kiasi cha muda Sarah mbio na biked.

    Jibu

    \(\frac{32r+32}{r(r+4)}\)

    Mfano\(\PageIndex{62}\)

    Ikiwa Pete anaweza kuchora ukuta katika masaa ya pp, basi kwa saa moja anaweza kuchora\(\frac{1}{p}\) ukuta. Itachukua Penelope masaa 3 zaidi kuliko Pete kuchora ukuta, hivyo saa moja anaweza kuchora\(\frac{1}{p+3}\) ukuta. Kuongeza maneno mantiki ya kupata\(\frac{1}{p}+\frac{1}{p+3}\) kujieleza kwa sehemu ya ukuta Pete na Penelope bila rangi katika saa moja kama kazi pamoja.

    Mazoezi ya kuandika

    Mfano\(\PageIndex{63}\)

    Donald anadhani kuwa\(\frac{3}{x}+\frac{4}{x}\) ni\(\frac{7}{2x}\). Donald ni sahihi? Eleza.

    Mfano\(\PageIndex{64}\)

    Eleza jinsi unavyopata Denominator ya kawaida ya\(x^2+5x+4\) na\(x^2−16\).

    Self Check

    ⓐ Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Picha hapo juu ni meza yenye nguzo nne na safu nne. Mstari wa kwanza ni mstari wa kichwa. Kichwa cha kwanza kinachoitwa “Naweza...”, pili “Kwa ujasiri”, ya tatu, “Kwa msaada fulani”, na ya nne “Hapana — Siipati!”. Katika safu ya kwanza chini ya “Naweza”, mstari unaofuata unasoma “ongeza maneno ya busara na denominator ya kawaida.”, mstari unaofuata unasoma “Ondoa maneno ya busara na denominator ya kawaida.”, mstari unaofuata unasoma, “Ongeza na uondoe maneno ya busara ambayo denominators ni kinyume.”, mstari wa mwisho unasoma “Je! orodha hii kukuambia kuhusu ustadi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?” Nguzo zilizobaki ni tupu.

    ⓑ Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?