Datrys 3x^{2}+5x+7+2x^3+3x+16/x^2+x=10x^3+12x+4/x-2+7x^3/x+1

$$3 x ^ { 2 } + 5 x + 7 + \frac { 2 x ^ { 3 } + 3 x + 16 } { x ^ { 2 } + x } = \frac { 10 x ^ { 3 } + 12 x + 4 } { x } - \frac { 2 + 7 x ^ { 3 } } { x + 1 }$$

Datrys ar gyfer x

$$x=3$$

Camau ar gyfer Datrys Hafaliad Llinol

All y newidyn x ddim fod yn hafal i unrhyw un o’r gwerthoedd -1,0 gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad wrth x\left(x+1\right), lluoswm cyffredin lleiaf x^{2}+x,x,x+1.

$$3x^{2}x\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Er mwyn lluosi pwerau sy’n rhannu’r un sail, adiwch eu esbonyddion. Adiwch 2 a 1 i gael 3.

$$3x^{3}\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 3x^{3} â x+1.

$$3x^{4}+3x^{3}+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Lluosi x a x i gael x^{2}.

$$3x^{4}+3x^{3}+5x^{2}\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 5x^{2} â x+1.

$$3x^{4}+3x^{3}+5x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Cyfuno 3x^{3} a 5x^{3} i gael 8x^{3}.

$$3x^{4}+8x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi x â x+1.

$$3x^{4}+8x^{3}+5x^{2}+\left(x^{2}+x\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi x^{2}+x â 7.

$$3x^{4}+8x^{3}+5x^{2}+7x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Cyfuno 5x^{2} a 7x^{2} i gael 12x^{2}.

$$3x^{4}+8x^{3}+12x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Cyfuno 8x^{3} a 2x^{3} i gael 10x^{3}.

$$3x^{4}+10x^{3}+12x^{2}+7x+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Cyfuno 7x a 3x i gael 10x.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi x+1 â 10x^{3}+12x+4 a chyfuno termau tebyg.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-x\left(2+7x^{3}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi x â 2+7x^{3}.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-\left(2x+7x^{4}\right)$$

I ddod o hyd i wrthwyneb 2x+7x^{4}, dewch o hyd i wrthwyneb pob term.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-2x-7x^{4}$$

Cyfuno 16x a -2x i gael 14x.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+14x+10x^{3}+4-7x^{4}$$

Cyfuno 10x^{4} a -7x^{4} i gael 3x^{4}.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=3x^{4}+12x^{2}+14x+10x^{3}+4$$

Tynnu 3x^{4} o'r ddwy ochr.

$$3x^{4}+10x^{3}+12x^{2}+10x+16-3x^{4}=12x^{2}+14x+10x^{3}+4$$

Cyfuno 3x^{4} a -3x^{4} i gael 0.

$$10x^{3}+12x^{2}+10x+16=12x^{2}+14x+10x^{3}+4$$

Tynnu 12x^{2} o'r ddwy ochr.

$$10x^{3}+12x^{2}+10x+16-12x^{2}=14x+10x^{3}+4$$

Cyfuno 12x^{2} a -12x^{2} i gael 0.

$$10x^{3}+10x+16=14x+10x^{3}+4$$

Tynnu 14x o'r ddwy ochr.

$$10x^{3}+10x+16-14x=10x^{3}+4$$

Cyfuno 10x a -14x i gael -4x.

$$10x^{3}-4x+16=10x^{3}+4$$

Tynnu 10x^{3} o'r ddwy ochr.

$$10x^{3}-4x+16-10x^{3}=4$$

Cyfuno 10x^{3} a -10x^{3} i gael 0.

$$-4x+16=4$$

Tynnu 16 o'r ddwy ochr.

$$-4x=4-16$$

Tynnu 16 o 4 i gael -12.

$$-4x=-12$$

Rhannu’r ddwy ochr â -4.

$$x=\frac{-12}{-4}$$

Rhannu -12 â -4 i gael 3.

$$x=3$$