Whakaoti i te 3/(2x+5)^2+4/(2x+1)^2=7/(2x+5)(2x+1)

$$\frac { 3 } { ( 2 x + 5 ) ^ { 2 } } + \frac { 4 } { ( 2 x + 1 ) ^ { 2 } } = \frac { 7 } { ( 2 x + 5 ) ( 2 x + 1 ) }$$

Whakaoti mō x

$$x = -\frac{17}{2} = -8\frac{1}{2} = -8.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{5}{2},-\frac{1}{2} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(2x+1\right)^{2}\left(2x+5\right)^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o \left(2x+5\right)^{2},\left(2x+1\right)^{2},\left(2x+5\right)\left(2x+1\right).

$$\left(2x+1\right)^{2}\times 3+\left(2x+5\right)^{2}\times 4=\left(2x+5\right)\left(2x+1\right)\times 7$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+1\right)^{2}.

$$\left(4x^{2}+4x+1\right)\times 3+\left(2x+5\right)^{2}\times 4=\left(2x+5\right)\left(2x+1\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x^{2}+4x+1 ki te 3.

$$12x^{2}+12x+3+\left(2x+5\right)^{2}\times 4=\left(2x+5\right)\left(2x+1\right)\times 7$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+5\right)^{2}.

$$12x^{2}+12x+3+\left(4x^{2}+20x+25\right)\times 4=\left(2x+5\right)\left(2x+1\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x^{2}+20x+25 ki te 4.

$$12x^{2}+12x+3+16x^{2}+80x+100=\left(2x+5\right)\left(2x+1\right)\times 7$$

Pahekotia te 12x^{2} me 16x^{2}, ka 28x^{2}.

$$28x^{2}+12x+3+80x+100=\left(2x+5\right)\left(2x+1\right)\times 7$$

Pahekotia te 12x me 80x, ka 92x.

$$28x^{2}+92x+3+100=\left(2x+5\right)\left(2x+1\right)\times 7$$

Tāpirihia te 3 ki te 100, ka 103.

$$28x^{2}+92x+103=\left(2x+5\right)\left(2x+1\right)\times 7$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+5 ki te 2x+1 ka whakakotahi i ngā kupu rite.

$$28x^{2}+92x+103=\left(4x^{2}+12x+5\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x^{2}+12x+5 ki te 7.

$$28x^{2}+92x+103=28x^{2}+84x+35$$

Tangohia te 28x^{2} mai i ngā taha e rua.

$$28x^{2}+92x+103-28x^{2}=84x+35$$

Pahekotia te 28x^{2} me -28x^{2}, ka 0.

$$92x+103=84x+35$$

Tangohia te 84x mai i ngā taha e rua.

$$92x+103-84x=35$$

Pahekotia te 92x me -84x, ka 8x.

$$8x+103=35$$

Tangohia te 103 mai i ngā taha e rua.

$$8x=35-103$$

Tangohia te 103 i te 35, ka -68.

$$8x=-68$$

Whakawehea ngā taha e rua ki te 8.

$$x=\frac{-68}{8}$$

Whakahekea te hautanga \frac{-68}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{17}{2}$$