Issolvi 3/(2x+5)^2+4/(2x+1)^2=7/(2x+5)(2x+1)

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

Solvi għal x

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -\frac{5}{2},-\frac{1}{2} billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(2x+1\right)^{2}\left(2x+5\right)^{2}, l-inqas denominatur komuni ta' \left(2x+5\right)^{2},\left(2x+1\right)^{2},\left(2x+5\right)\left(2x+1\right).

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2x+1\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 4x^{2}+4x+1 b'3.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2x+5\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 4x^{2}+20x+25 b'4.

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

Ikkombina 12x^{2} u 16x^{2} biex tikseb 28x^{2}.

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

Ikkombina 12x u 80x biex tikseb 92x.

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

Żid 3 u 100 biex tikseb 103.

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

Uża l-propjetà distributtiva biex timmultiplika 2x+5 b'2x+1 u kkombina termini simili.

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

Uża l-propjetà distributtiva biex timmultiplika 4x^{2}+12x+5 b'7.

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

Naqqas 28x^{2} miż-żewġ naħat.

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

Ikkombina 28x^{2} u -28x^{2} biex tikseb 0.

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

Naqqas 84x miż-żewġ naħat.

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

Ikkombina 92x u -84x biex tikseb 8x.

$$8x+103=35$$

Naqqas 103 miż-żewġ naħat.

$$8x=35-103$$

Naqqas 103 minn 35 biex tikseb -68.

$$8x=-68$$

Iddividi ż-żewġ naħat b'8.

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

Naqqas il-frazzjoni \frac{-68}{8} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 4.

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