NCTB Class 7 Math Chapter six Exercise 6.1 Solution by Math Expert. Bangladesh Board Class 7 Math Solution Chapter 6.1 “Algebraic Fractions” Exercise 6.1 Solution.

Board |
NCTB |

Class |
7 |

Subject |
Math |

Chapter |
Six |

Chapter Name |
“Algebraic Fractions” |

Exercise |
6.1 Solution |

**Exercise:- 6.1**

**(1) Solution:-** a^{2} b/a^{3} c

= b/ac

**(2) Solution:-** a^{2} b c/ab^{2} c

= a/b

**(3) Solution:-** x^{3}y^{3}z^{3}/x^{2}y^{2}z^{2}

= x y z

**(4) Solution:-** x^{2}+x/x y +y

= x(x+1)/y(x+1)

= X/y

**(5) Solution:-** 4a^{2} b/6a^{3} b

= 4/6x a^{2} b/a^{3} b

= 2/3×1/a

= 2/3a

**(6) Solution:-** 2a-4ab/1-4b^{2}

= 2a (1-2b)/(1)^{2}– (2b)^{2}

= 2a (1-2b)/(1+2b) (1-2b)

= 2a/(1+2b)

**(7) Solution:-** 2a+3b/4a^{2}-9b^{2}

= 2a+3b/(2a)^{2} – (3b)^{2}

= 2a+3b/(2a+3b) (2a-3b)

= 1/2a-3b

**(8) Solution:-** a^{2}+4a+4

= a^{2}+2a+2a+4/(a)^{2} – (2)^{2}

= a(a+2)+2 (a+2)/(a+2) (a-2)

= (a+2) (a+2)/(a+2) (a-2)

= (a+2)/(a-2)

**(9) Solution:-** x2-y2/(x +y)2

= (x +y) (x-y)/ (x +y) (x +y)

= X-y/x +y

**(10) Solution:-** x^{2}+2x-15/x^{2} +9x+20

= x^{2}+5x-3×15/x^{2}+5x+4x+20

= X(x+5) -3 (x+5)/x (x-5) +4 (x+5)

= (x+5) (x-3)/(x+5) (x+4)

**(11) Solution:-** a/b c, d/a c

Denominator b c 8 ac, L.C.M= a b c

Therefore, a/ac = a x a/b c x a

= a^{2}/a b c

And a/ac = a x b/a c x b

= a b/a b c

**(12) Solution:-** x/p q, y/p r

L.C.M of denominator = p q r

Therefore, x/p q = x X r/p q x r = x r/p q r

y/p r= y X x/p r x q = y q/p q r

**(13) Solution:-** 2x/3m, 3y/2n

L.C.M of denominator= 6mn

Therefore, 2x/3m = 2xX2n/3mx2n= 4xn/6n

= 3y/2n = 3yx3m/2mx3m= 9my/6mn

**(14) Solution:-** a/a-b, b/a +b

Therefore, L.C.M of denominator (a +b) (a-b)

Therefore, a/a-b= a x(a +b)/(a-b) (a +b) = a(a +b)/a^{2} – b^{2}

=> b /a +b = b x(a-b)/(a +b) (a-b) = b(a-b)/a^{2} – b^{2}

**(15) Solution:-** x^{2}/a^{2}-2ab, y^{2}/a+2b

Therefore, L.C.M of denominator= (a+2b) (a^{2}-2ab)

= (a+2b) (a-2b)a

Therefore, x^{2}/a^{2}-2ab= x^{2}X(a^{2}+2ab)/(a^{2}-2ab) (a^{2}+2ab)= x^{2} (a^{2}+2ab)/a (a^{2}-4b^{2})

=> y^{2}/a+2b= y^{2}xa (a-2b)/(a+2b) (a-2b)a = ay^{2} (a-2b)/a (a^{2}-4b^{2})

**(16) Solution:-** 3/a^{2}-4, 2/a (a+2)

L.C.M, of denomination, = (a^{2}-4) a (a+2)

= a (a+2) (a-2)

3/a^{2}-4 = 3xa/(a+2) (a-2)a

= 3a/a(a2-4)

2/a(a+2) = 2(a-2)/a(a+2) (a-2)

= 2 (a-2)/a(a^{2}-4)

**(17) Solution:- **a/a^{2}-9, b/a+3

Therefore, a^{2}-9, (a)^{2} – (3)^{2} = (a+3) (a-3)

L.C.M of denominator= a (a+3) (a-3)

a/a^{2}-9 = a. 1/(a+3) (a-3) = a/a^{2} – 9

= b/(a+3) = b(a-3)/(a+3) (a-3) = b(a-3)/a^{2} -9

**(19) Solution:-** a/a-b, b/a +b, c/a(a +b)

L.C.M, of denominator = a (a +b) (a-b)

a/ a-b = a x a(a +b) /(a-b) a(a +b)= a^{2}(a +b)/a(a^{2}-b^{2})

b /a +b= b x a (a-b)/(a +b) x a (a-b) = a b(a-b)/a (a^{2}-b^{2})

c/a (a +b) = c x(a-b)/a (a +b) (a-b) = c(a-b)/a (a^{2}-b^{2})

**(20) Solution:-** 2/x^{2}– x- 2, 3/x^{2}+x-6

= x^{2}-x-2 = (x+1) (x-2)

X^{2}+x-6= (x-3) (x-2)

Therefore, (x+1) (x-2) (x+3)

Therefore, 2/x^{2}-x-2= 2x(x+3)/(x+1) (x-2) x (x+3)

3/x^{2}+x-6 = 3x(x+1)/(x+3) (x-2) (x-1)