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simplify the following
- (x5)7
=x35 - y9⋅y4
=y13 - (3a7)4
=81a28 - 7x11⋅8x15
=56x26 - (25x31)23
=125x21 - 14a53⋅12a−91
=168a4522
- (x5)7
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simplify the following
- 32x+23x
=64x+9x
=613x - 23a−4a
=45a - 43x−6y−3x
=129x−2y−4x
=125x−2y - x3+y2
=xy3y+2x - x−23+x+12
=(x+1)(x−2)3(x+1)+2(x−2)
=(x+1)(x−2)3x+3+2x−4
=(x+1)(x−2)5x−1 - x−13+(x−1)(x+4)2
=(x−1)(x+4)3(x+4)+2
=(x−1)(x+4)3x+14 - x−23−x+22+x2−44
=(x−2)(x+2)3(x+2)−2(x−2)+(x−2)(x+2)4
=(x−2)(x+2)3x+6−2x+4+4
=(x−2)(x+2)x+14 - x+25+x2+5x+63−x+32−x
=(x+3)(x+2)5(x+3)+3−(x+2)(2−x)
=(x+3)(x+2)5x+18−(−x2+4)
=(x+3)(x+2)5x+18+x2−4
=(x+3)(x+2)x2+5x+14 - 2x−y−x−y1
=2(x−y)(x−y)2−2
=2x−2yx2−2xy−y2−2 - x−13−1−x4x
=x−13+4x - x2+3x+22+x2+7x+103
=(x+1)(x+2)2+(x+2)(x+5)3
=(x+1)(x+2)(x+5)2(x+5)+3(x+1)
=(x+1)(x+2)(x+5)5x+13 - 2x2+x−3x−2x2−5x−125
=(2x+3)(x−1)x−(2x+3)(x−4)5
=(2x+3)(x−1)(x−4)x(x−4)−5(x−1)
=(2x+3)(x−1)(x−4)x2−9x+5 - x+35+3x−24x+2−3x2
=x+35+3x−24x−2
=(x+3)(3x−2)15x−10+(x+3)(4x−2)
=(x+3)(3x−2)15x−10+4x2−2x+12x−6
=(x+3)(3x−2)4x2+25x−16 - 4−x5−x+x+43x+1−x−42
=x−4x−7+x+43x+1
=(x−4)(x+4)x2−3x−28+3x2−11x−4
=(x−4)(x+4)4x2−14x−32 - 3x2+5x−2x−3+−3x2+16x−54−2x
=3x2+5x−2x−3+3x2−16x+52x−4
=(3x−1)(x+3)x−3+(3x−1)(x−5)2x−4
=(3x−1)(x+3)(x−5)x2−8x+15+2x2−x−12
=(3x−1)(x+3)(x−5)3x2−9x+3
- 32x+23x
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simplify the following
- 2xx2⋅x4y3
=2y3 - 4y3x2⋅6xy2
=8xy - 2yx2÷63xy
=y2x - 3a4−x⋅4−xa2
=3a - x2+3x−4(x−1)2
=x+4x−1 - x−3x2−x−6
=x+2 - xx−2÷2x2x2−4
=x−42x−4 - x2−3xx+2÷x2−4x+34x+8
=x(x−3)x+2⋅4(x+2)(x−3)(x−1)
=xx−1 - x−12x÷x2−14x2
=x−12x⋅4x2(x+1)(x−1)
=2x+1 - x+2x2−9⋅x−33x+6÷x9
=x+2(x+3)(x−3)⋅x−33(x+2)⋅9x
=3x2+3x - 9x−63x÷x−26x2⋅x+52
=9x−63x⋅6x2x−2⋅x+52
=x(9x2+39x−30)x−2 - x2+x2x2+3x−5÷x2+2x+12x2+7x+5
=x(x+1)(2x+5)(x−1)⋅(2x+5)(x+1)(x+1)(x+1)
=xx−1 - 3x+5x+2⋅x2−46x+10÷4−2x8x
=3x+5x+2⋅(x+2)(x−2)2(3x+5)⋅8x4−2x
=4x(x−2)4−2x - 4−x2x2−9÷x2+x−63+2x−x2
=(2−x)(2+x)(x+3)(x−3)⋅(x+3)(−x−1)(x+3)(x−2)
=(2−x)(x+2)(−x−1)(x+3)(x−3)(x−2) - x2+2x2x2+x−3÷x2x2−4x+3÷x2−x−62x2+3x
=x(x+2)(2x+3)(x−1)⋅(x−3)(x−1)x2⋅x(2x+3)(x−3)(x+2)
=1
- 2xx2⋅x4y3
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solve the following equations
- 3x−2=−7
3x=−5
x=−15 - 45x−2+21=−2
45x−2=−25
5x−2=−10
5x=−8
x=5−8 - 45x−1=73
5x=740
x=78 - 32x−1=75x+1
14x−7=15x+3
x=−10 - 32x+1+7=11
2x+1=12
x=211 - 32x+1+7=43x−1
4(2x+1+37)=9x−3
8x+4+328=9x−3
x=7+328
x=349 - 5x+2+2x−1=3x+1
102x+4+5x−5=3x+1
6x+12+15x−15=10x+10
11x=13
x=1113 - x+5=x14
x2+5x−14=0
(x+7)(x−2)=0
x=2∨x=−7 - 3x+1=x10
x2+x=30
x2+x−30=0
(x+6)(x−5)=0
x=−6∨x=5 - x+11=6x5x−6
6x=5x2−6x+5x−6
0=5x2−7x−6
0=(5x−3)(x+2)
x=53∨x=−2 - 32x+15x−1=32+x22
1511x−1=3x2x+66
33x2−3x=30x+990
33x2−33x−990=0
x2−x−30=0
(x+5)(x−6)=0
x=−5∨x=6 - 7x+1+x−28=3
7x−14x2−x−2+56=3
x2−x−2+56=21x−42
x2−22x+96=0
(x−6)(x−16)=0
x=6∨x=16
- 3x−2=−7
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express the following as a single fraction
- 1−x+1−x2
=1−x+1−x21−x
=1−x31−x - x−42+32x−4
=3x−46+3x−42(x−4)
=3x−42x−2 - x+43+x+42
=x+45 - x−53+x−5
=x−53+x−5x−5
=x−5x−2 - 2x−13x3−3x22x−1
=2x−13x3−2x−13x2(2x−1)
=2x−13x3−6x3+3x2
=2x−1−3x3+3x2 - 3x+34x4+3x2x+3
=3x+34x4+3x+39x2(x+3)
=3x+34x4+9x3+27x2
- 1−x+1−x2
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express the following as a single fraction
- (6x−3)31−(6x−3)−32
=(6x−3)31−(6x−3)321
=(6x−3)326x−3−(6x−3)321
=(6x−3)326x−4 - (2x+3)41−2x(2x+3)−43
=(2x+3)41−(2x+3)432x
=(2x+3)432x+3−2x
=(2x+3)433 - (3−x)−52−5x(3−x)53
=(3−x)521−(3−x)525x(3−x)
=(3−x)525x2−15x+1
- (6x−3)31−(6x−3)−32