Issolvi x+6/x-5+x-5/x+6=2x^2+23x+4/x^2+x-30

$$\frac { x + 6 } { x - 5 } + \frac { x - 5 } { x + 6 } = \frac { 2 x ^ { 2 } + 23 x + 4 } { x ^ { 2 } + x - 30 }$$

Solvi għal x

$$x = \frac{19}{7} = 2\frac{5}{7} \approx 2.714285714$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -6,5 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-5\right)\left(x+6\right), l-inqas denominatur komuni ta' x-5,x+6,x^{2}+x-30.

$$\left(x+6\right)\left(x+6\right)+\left(x-5\right)\left(x-5\right)=2x^{2}+23x+4$$

Immultiplika x+6 u x+6 biex tikseb \left(x+6\right)^{2}.

$$\left(x+6\right)^{2}+\left(x-5\right)\left(x-5\right)=2x^{2}+23x+4$$

Immultiplika x-5 u x-5 biex tikseb \left(x-5\right)^{2}.

$$\left(x+6\right)^{2}+\left(x-5\right)^{2}=2x^{2}+23x+4$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+6\right)^{2}.

$$x^{2}+12x+36+\left(x-5\right)^{2}=2x^{2}+23x+4$$

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

$$x^{2}+12x+36+x^{2}-10x+25=2x^{2}+23x+4$$

Ikkombina x^{2} u x^{2} biex tikseb 2x^{2}.

$$2x^{2}+12x+36-10x+25=2x^{2}+23x+4$$

Ikkombina 12x u -10x biex tikseb 2x.

$$2x^{2}+2x+36+25=2x^{2}+23x+4$$

Żid 36 u 25 biex tikseb 61.

$$2x^{2}+2x+61=2x^{2}+23x+4$$

Naqqas 2x^{2} miż-żewġ naħat.

$$2x^{2}+2x+61-2x^{2}=23x+4$$

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

$$2x+61=23x+4$$

Naqqas 23x miż-żewġ naħat.

$$2x+61-23x=4$$

Ikkombina 2x u -23x biex tikseb -21x.

$$-21x+61=4$$

Naqqas 61 miż-żewġ naħat.

$$-21x=4-61$$

Naqqas 61 minn 4 biex tikseb -57.

$$-21x=-57$$

Iddividi ż-żewġ naħat b'-21.

$$x=\frac{-57}{-21}$$

Naqqas il-frazzjoni \frac{-57}{-21} għat-termini l-aktar baxxi billi testratta u tikkanċella barra -3.

$$x=\frac{19}{7}$$